There are a variety of factors that contribute to this phenomenon, as you might expect.

1. This was a time period of the most internal conflict the country has seen for most of its history. William Henry Harrison is a bit of an outlier (he died after a month) but almost every president had to oversee dramatic internal or external conflict. Almost all of these conflicts can be tied back to slavery or connections to slavery. Tyler (and the several before him) had to deal with the annexation of Texas, and what that could mean in terms of expanding slavery. Polk expanded the country a la manifest destiny, but there was a minority who resisted the Mexican-American War. We also see the Wilmot Proviso, in 1846, basically splitting Congress and the political parties (Democrats and Whigs) along slave/free lines -- and this is long before the war even ends. Then there is the overall conflict over adding California as a free/slave state when it is divided in half by the Missouri Compromise line. Taylor only served for about 15 months before dying in office, but his goal was to achieve sectional harmony rather than any major policy. Then we have Fillmore, who completed Taylor's term, but essentially oversaw the demise of the national Whig Party (which was continuing to splinter over slave/free lines set into action by the Wilmot Proviso). He also was president while the Compromise of 1850 was passed, which caused major internal strife over the Fugitive Slave Law that basically deputized northerners into returning escaped southern slaves. Next, we have Pierce, who oversaw the push of popular sovereignty towards the Kansas and Nebraska territories, and the actions during Bleeding Kansas, where actual violence between slave and free sides was a bit of a preview of the Civil War. This event also leads to the creation of the Republican Party out of bits of other parties (Free Soil, antislavery Whigs, northern antislavery Democrats) whose sole purpose is to stop the spread of slavery, not slavery entirely. Buchanan was elected basically on the premise of "I was in Europe during the whole Kansas ordeal" and he stuck by his belief that the president constitutionally had no power to intervene in state issues. The raid on Harpers Ferry by John Brown, a man who was already infamous for leading a group who murdered pro-slavery supporters during Bleeding Kansas, happens during Buchanan's presidency, further heightening the southern belief that all northerners and abolitionists threaten their way of life. Lincoln, on the other hand, had no such qualms about expanding presidential power during a crisis; he did oversee the Civil War, but he often overreached his constitutionally approved power (ending habeus corpus, instituting martial law in Maryland, etc. depending on the historian you talk to, Lincoln is either praised or demonized for these events) in order to achieve his goal of keeping the Union together. Obviously, the first Republican president Lincoln dies in office, but Johnson is one of the few southern Democrats (from Tennessee) who remained loyal to the Union, so his take on Reconstruction after the war is a little too soft for the Republicans' liking. (He was ticketed as Lincoln's vice president as a way to make sure an antiwar candidate didn't win the presidency over Lincoln.) Johnson ends up getting impeached, but as he is not seeking re-election, the congressional Republicans let him ride out the few months until the election of 1868. Then, Grant (who is moderately successful in terms of continuing Reconstruction) has one of the most corrupt presidencies in history, rivaling Harding's. The Whiskey Ring and the Credit Mobilier scandal are the major ones there.

So, if we look at this list, each president has a major conflict over slavery or the immediate impact of the Civil War, or they died early in their presidency, except for Grant, who has corruption in spades. All of these slavery-related conflicts cause increasing sectionalism between the South and the North/the West, and increasing violence. It is difficult to consider domestic issues a win for most of these presidents while this is going on. This is a bit of a revisionist view, but seeing as these presidents' actions did little to actually prevent a Civil War (at best delaying it), the pre-CW presidents are not viewed kindly by history, especially Buchanan. This leads me back to another commonality in this era of the presidency...

2. The lack of 'imperial presidency.' I mentioned this specifically with Buchanan, but the presidency during this era is different than we think of it in the modern day. Essentially, the idea here is that prior to FDR, most presidents had very few staff members, so their impact on legislation and events in the country was less wide-ranging than modern presidents. Some historians argue that the most recent presidents also have expanded the use of their executive powers to combat an unwilling or ineffective Congress. Prior to 1877, most presidents simply don't believe they have the right or the power to heavily interfere with legislation, only its enforcement. From Harrison to Grant, there were 158 vetoes, of which 25 were overridden by Congress, or 16%. Of those 158, the majority (122) were under Johnson (who, remember, was the opposite party of the president he ended up replacing, and at odds with an almost entirely Republican Congress) and Grant. Most of the presidents prior to the Civil War simply felt that policy-making was mostly outside the realm of their power, even if it caused an increase to sectionalism, so they frequently avoided interacting with it. (In contrast, Grover Cleveland had 584 vetoes, FDR had 635, and Truman had 250. While vetoes aren't always a measure of presidential power, it does demonstrate that many of these early presidents tended to not interfere with the legislative process.) In modern media, almost everything that happens during a presidency is ascribed to the president himself, but in actuality, most presidencies rely heavily on the cooperation of Congress to get their agenda through.

3. The makeup of Congress means that all the locally elected leaders in the House (and similarly the Senate, who at this point is still elected by the state governments) have to make national policy. The balance of this is tricky, and often fails to appease both sides. Therefore, this is a recipe that often leads to sectional interests taking hold, especially in the era of slave/free conflict. If I'm a representative from Alabama, I sure as hell don't care what people in Massachusetts think of me, I only care what the voters of Alabama think of me. The obviously limited suffrage of only white men also further heightens the stakes on the slavery issue -- the only voters these people care about are well, people who can actually vote. All of this combines into a large blender of sectionalism and slavery. Because of all of this, it falls to one man to be the "national" leader who ends sectionalism -- the president. However, often, the President is elected by sectional interests, so even these cases can be tricky. Lincoln wins in 1860 despite not being on the ballot in many Southern states. Likewise, Buchanan is elected by an almost exact north/south divide, though the line where the divide is located is further north on the map than 4 years later.

All of these factors combine to make it difficult for presidents to achieve national unity and to avoid conflict over slavery. Also, the presence of slavery and the inherent racism in the concept of manifest destiny cause some of the more successful presidents (Polk) to be weighed down in ratings conducted with the benefit of hindsight. We can contrast this with most other periods in American history, where literally no other Civil War takes place. Were there to be actual internal warfare during some of the more contentious periods (War of 1812 with Hartford Convention; Civil Rights movements in 1950s and 1960s), I am certain the presidents who did not "prevent" these hypothetical wars would also receive quite a hit in their ratings as well.

Sources:

Schlesinger, Arthur M. The Imperial Presidency, 1973.

Karabell, Zachary. "How the GOP Made Obama One of America's Most Powerful Presidents," Politico, April 14, 2016. https://www.politico.com/magazine/story/2016/04/barack-obama-gop-most-powerful-213814

https://www.senate.gov/reference/Legislation/Vetoes/vetoCounts.htm

Arnove, Anthony, and Zinn, Howard, eds. Voices of a People's History of the United States, 2004. (for resistance to Mex-Am War)

Newman, John J., and Schmalbach, John M. United States History: Preparing for the Advanced Placement Examination, 2016. (for the overall events tied to each presidency, sorry if this source is of dubious quality -- this is my course's textbook and I know this covers all the events)

Rating presidents is a deeply subjective exercise because there are so many metrics you can choose between. This lot mostly have a big one in common, so let's look at that.

Most of them were successful and that's the problem; they were successes at terrible things. With the exceptions of Lincoln and Grant, they're all proslavery men. Their chief job is shoring up their support in the slave states, either because it's literally their base or because they need a strong southern showing to win and keep the presidency in the first place. A few are general failures by some metric and most of them except Lincoln are really bad at the test of "can you maybe not work so hard to cause a Civil War?"

William Henry Harrison outright died before he could accomplish anything, which makes him ineffective even were he a master politician that otherwise had Washington wound around his little finger.

John Tyler's accidental presidency is a hot mess. He was a Whig, sort of, but really a radical proslavery man -which puts him in good company even among Whigs- who happened to oppose almost the whole Whig party agenda. National bank? Not on Tyler's watch! He spent a lot of his presidency fighting with the Whigs in Congress, who basically read him out of the party. At that point, even if Tyler wanted to do otherwise, he needed a new set of supporters and decided he would get them by going all-in on slavery expansion. That didn't work out so well for him because the Democrats already had the market cornered and why would they vote for him when they could have one of their own? The dodgy way he forced through Texas annexation -a joint resolution of Congress rather than a treaty because he couldn't get 2/3 of the Senate to agree- didn't help.

Texas annexation leads fairly directly to the Mexican War, which inaugurates the traditional grand battle over the fate of slavery in the West. It's actually gone on before this -that's why Texas didn't get annexed when it asked in 1836- but from about 1846 onward it becomes the overt, dominant national issue. The whole point of the Second Party System was to contain and neutralize antislavery politics, so Tyler's annexation gets the ball rolling in a lot of ways. And this is something that he couldn't have missed since it was a major theme of politics around the annexation of Texas for a good decade before he got his way.

James K. Polk had, in many senses, the most successful presidency ever. It was a disastrous success, just as he planned. He would say it wasn't disastrous at all, but he was a proslavery man working hard to expand slavery. In theory, he was a general expansionist but he happily accepted a negotiated settlement with the UK over the Canadian boundary and then staged a war so he could relieve Mexico of vast tracts of territory that it claimed on the grounds of both Texas ludicrous boundary claims (all the way to the Rio Grande...in the West) and the whole rest of the Southwest while he was at it basically because he could. He intrigued heavily, if incompetently, for the purchase of Cuba too. All that new land means that the nation needs to decide if slavery will go out there or not, which occasions new escalations on both sides even separate those that Texas itself brought in. Many antislavery whites were willing to reluctantly call a mulligan on Texas, including David Wilmot who otherwise wanted every inch of dirt the US collected from Mexico to have slavery banned, but the future California, Utah, Nevada, Arizona, and New Mexico were up for grabs now too.

Zachary Taylor had a bit of the same problems that Tyler and Harrison had. Takes on him vary, but most historians consider him the good slaveholding Whig president. He took firm stands against southern brinksmanship over the Mexican War spoils and planned to get New Mexico and California both into the Union as free states, with the two covering the entire American Southwest, minus Texas. He may have been taking cues from William Seward, New York's antislavery Senator. Or he might have been a seriously proslavery man who expected an eventual settlement much like the Compromise of 1850, which is the minority view. Either way, there's some debate over whether his hard line against Texas' grander territorial claims was him showing good, firm resolve or if it was wildly irresponsible brinksmanship that risked igniting a civil war then and there. Then he ate some bad cherries and died.

That brings us to Millard Fillmore, who signed off on the whole Compromise of 1850. The most important and odious part of that is a new Fugitive Slave Law that criminalizes aiding slaves who escaped to free states and imposes heavy penalties for it, whilst simultaneously depriving accused fugitives of any real due process and offering a kickback to the new judges appointed to order their renditions.

Fillmore did not win the Whig nomination to a term of his own, so Winfield Scott got to head the last ever Whig presidential ticket and lose to Franklin Pierce. Franklin Pierce is terrible. He was a proslavery hatchet man in New Hampshire. He had just enough judgment to know that signing a repeal of the Missouri Compromise in the Kansas-Nebraska Act would be a political disaster. He expressed his opposition to the scheme in public. Then he allowed himself to be conned and steamrolled into pushing hard for it and signing the bill into law. That inaugurated Bleeding Kansas, with proslavery and antislavery militants flooding into the territory to settle its fate. Presented with that problem, Pierce went out of his way to side with the proslavery party even when they were armed bands from Missouri who came to Kansas and voted illegally, outlawed political opposition to slavery, and initiated most of the violent political clashes in the territory up through the middle of 1856. John Brown gets all the press, but proslavery militants straight up murdered people at least a year before he ordered some men dragged out of their homes at night to be hacked up with artillery swords. Antislavery militants to that point where usually happy to just burn your cabin down while you were away. None of that happens if Pierce either vetoed the bill or refused to make it a test of Democratic party loyalty. Bleeding Kansas wasn't a literal goal for Pierce, but he did little to improve it and much to make it worse.

James Buchanan is another mess. His main qualification, a /u/wat21 notes, was in that he had been out of the country for four years. The other one, and it's a biggie, is that James Buchanan made his career being slavery's best friend in the North. The only way you could be more pliable and inclined to do a solid for slavery than James Buchanan was by actually owning people yourself, which one contemporary Indiana senator actually did. We don't know for sure, but it's possible that he influenced the outcome of the Dred Scott decision which outlawed the platform of his opposing party. He inherited Bleeding Kansas and worked hard to make sure the proslavery side got to keep its ill-gotten gains. He failed and split his own party in the doing, which contributed to the GOP win in 1860. That in turn brought about the final slavery crisis, which he did little to combat.

Abraham Lincoln routinely wins top spot in rankings of presidents. He's also where my detailed study largely ends.

To begin, a quote from Abraham Lincoln: "You cannot escape the responsibility of tomorrow by evading it today."

The string of Presidents experienced in the post Jacksonian and pre Civil War United States are looked down upon so unfavorably because they or their administrations often held immense opportunities to steer the United States in a direction that would not have resulted in the Civil War. These opportunities would slip through the cracks repeatedly due to political expediency or desire to ensure communion with their parties.

We begin with the most brief of these administrations with William Henry Harrisons, his was a presidency of expediency for the Whigs who sought to reverse their perceived lack of unity which actually enabled Harrison's opposition Martin Van Buren to defeat no less then 3 separate Whig candidates and get elected in his own right in 1836.

Harrison was an amicable man of good reputation for his service in the War of 1812 and his administration was intended to be a repudiation of Jacksonian concepts like the Patronage System and their abolition of the Bank of the United States. Harrison elaborated in great detail about this. So much so that his speech elaborating on this was about 8400+ words. A record length at the time and a speech that ironically would prevent him from enacting any of these platforms. He would die from pneumonia that he most likely contracted due to the damp and wet weather of the day he was inaugurated and gave his long speech. Without a coat of course.

John Tyler, his successor would prove much more a formidable opponent to his own party then anyone else in the post Jacksonian period. Unlike Harrison he was disgusted at the willingness of Whigs to simply take over rather then abolish Jackson's patronage system and would frequently clash with Senator Henry Clay (A founder of the Whig's and great statesmen in his own right) over the matter of who decided policy, the Congress or the executive. These clashes would see many of Tyler's own cabinet resign and his presidency fatally wounded when the Whigs politically marooned him by expelling him from the party.

Tyler would thereafter spend the remainder of his term unable to move any domestic policies due to none in Congress seeing him as an ally. Effectively castrated on the domestic front, Tyler would focus his energies into foreign affairs. Achieving landmark reconciliation with the United Kingdom through the Webster–Ashburton Treaty.

Tyler like all Presidents until Lincoln following Jackson would be a one term president. Intent on fighting on without the nominations of either party, he would quickly consign himself to a graceful exit instead by endorsing James K. Polk of the Democratic party who shared his vision of annexing the break off region of Mexico in Texas. And indeed his most consequential action was among his last, in the transitional period as a "lame duck" President Tyler would ratify the legislation to annex Texas while the process would be fulfilled by his successor.

Unlike Harrison, Tyler was a staunch constitutionalist and was a strong supporter of the states right to possess slaves. He also as a sign of his failure to gain the support of either party has the dubious distinction of being the first President to see his veto overturned by Congress.

Polk's presidency was a return to several Jacksonian era ideas and more importantly to that of expansionism. Under Polk not only would Texas be gained but so too would be nearly all of the contemporary Western United States. A man of great vision and resolve, his was not a failure of nerve but instead a lack of ambitions towards that end. Polk was a native of Tennessee and was a firm believer in slavery, even purchasing many of his slaves during his time in the executive office.

He entered office with 4 defined goals:

• Reestablish the Independent Treasury System which the Whigs had done away with.

• Reduce tariffs.

• Acquire some or all of the Oregon Country.

• Acquire California and its harbors from Mexico.

And in all of these goals Polk succeeded in fulfilling his ambitions. He successfully resolved an outstanding dispute with the British Empire in laying claim to the Oregon and Washington territories and as well saw the Mexican border driven from Idaho to the River Grande. Indeed Polk was close to achieving the further ambition of annexing Mexico itself until his ambitions were rendered asunder by his diplomat receiving this directive too late.

Polk's great expansion in the Mexican-American war resumed and exacerbated the great debate as to the future of the nation and wherein the frontier of slavery lay. He consigned himself to one term intentionally however and refused to accept any nomination while bitter divides in the Democratic party between it's increasingly anti slavery northern wing and the southern dominated mainstream wing resulted in a split vote for the 1848 election. Polk was succeeded by a successful general in the war he begun with Zachary Taylor.

A populist by intent, Taylor rode his star power acquired during the Mexican-American War to office with the ambition of remaining aloof and keeping the Union from destroying itself. To this end he was largely a success and while a slaveholder and southerner himself he actually refrained from advocating for slaveries expansion within the union.

To avoid the issues that plagued the final year of the Polk administration with the debate over the expansion of slavery Taylor would back moves to admit New Mexico and California directly into the Union. Though this would not occur in his lifetime with the compromise only directly being enacted after his demise, the admission of California to the union also allowed for the dispute of boundaries between Texas and New Mexico to be resolved. Creating the current borders.

Taylor was a flawed man like many presidents, but he is only looked upon in an unremarkable sense due to the longevity of his administration which scarcely exceeded 18 months. Taylor's presence reaffirmed the convictions of the union to be upheld (By force if necessary). He was to have said concerning any secessionists: "taken in rebellion against the Union, he would hang ... with less reluctance than he had hanged deserters and spies in Mexico."

The same cannot be said of his successor Millard Fillmore. Who while much more morally inclined against slavery also imagined it was not within constitutional boundaries that the Federal Government could act against it. Fillmore's enforcement of the controversial Fugitive Slave Act (1850) effectively ensured the split between northern and southern Whigs. Killing in all but name the former principle rival to the democrats. Fillmore achieved some things of note, particularly opening up Japan to trade with the Perry Expedition which heralded events that lead to a modernized Japan before the centuries end. But otherwise his presidency proved not sufficiently energetic enough for the Whigs who passed him over for their nomination. They instead chose who they perceived to be another Taylor with his fellow General from the Mexican-American War Winfield Scott.

The perceived flopping of the Whigs was too great for the public to grant them another mandate however. They instead chose Democratic candidate Franklin Pierce. A northerner who perceived abolitionism as a possible fatal wound to the Union.

Pierce would spend his term reaffirming pro slavery sentiments across America and by seeking the acquisition of more lands from Mexico to develop railroads and also the annexation of Cuba from Spain. A reality that for the former resulted in the Gadsden purchase and in the latter would not be seen until William McKinley nearly 50 years later.

Pierce would confront his greatest domestic challenge with "Bleeding Kansas" where the white settlers fought among themselves to try and achieve their preferred status of slavery in the territory upon statehood. Pierce straddled the line of which he would support and instead passed the Kansas-Nebraska Act with Senator Stephen Douglas of Illinois. This would provide the mechanism by which a vote could occur on the matter instead.

The pro slavery elements won by dubious distinction of bringing in enough voters from slave state Missouri to win and stack the legislature with Democrat. After this chicanery was exposed the local free soilers established a legislature parallel to the pro slavery one in Kansas. One Pierce regarded as an act of rebellion against the United States and used federal troops to disperse with force.

With the Democrats suffering monumental losses in everywhere but the South despite the Whig's also faltering, Pierces remarkably divisive and failed Presidency was given an expiration date of the Democratic national convention. Despite these circumstances, Franklin Pierce imagined he would be renominated which he was sorely mistaken in.

Pierce would earn the distinction of being the only elected incumbent president to lose the nomination for re election in his own party. The aloof James Buchanan managed to get the nomination with the support of Stephen Douglas despite Pierce attempting to push the latter to the nomination as an act of revenge. Pierce therefore left office a bitter man. In his final speech to congress he railed against the Republicans and Whigs about his success on the fiscal front and his maintenance of the peace.

His successor Buchanan was elected by a much more narrow margin then Piece was but he benefited from the Republicans having to contest with the final remnants of the Whig's in Millard Fillmore's "Know nothing" bid for the Presidency.

I'm out of space to underline how disastrously Buchanan's presidency ensured the previous 30 years would be looked upon unfavorably by Americans following the civil war. But many of these presidents were balanced if benign constitutionalists that simply lacked the political capital to challenge things.