Reliability and the cost of maintenance, mostly. Lever-actions are more complicated, which makes them difficult to clean (especially in the field), expensive to maintain, and expensive to manufacture. Because much of the lever is on the bottom of the rifle, it makes it much easier for mud and dirt and what-have-you to work its way into the mechanism.

Bolt-actions are, in general, quite a lot less complicated, easier to clean and maintain, and easier for soldiers to use. Rate of fire was not much of a concern for most armies until the 20th century, believe it or not. I wrote a bit more about it in this thread.

David F. Butler, United States Firearms: The First Century: 1776-1875

Not to discourage further discussion, but this has come up a few times; most recently [here] (https://www.reddit.com/r/AskHistorians/comments/6q7axm/whenever_i_hear_about_famous_firearms_it_seems/) answered by u/Mrprocrastinaut

As it happens, this is a question I have been researching lately. I am going to concentrate on the decision making of the U.S. army. Hopefully someone better informed about rifle development in other countries will shed some light there.

The first successful magazine repeater in the world was the 1860 model Henry rifle, which used a lever action. While a couple of thousand of these rifles were bought and used by individual soldiers during the American civil war (1860-1865), neither side officially adopted it. The union army despaired of being able to acquire enough cartridges to keep these rapid fire guns supplied, and the confederacy's supply difficulties were considerably more severe than the union's. The union army did acquire enough Sharps lever action single shot breechloaders to equip several units, about 11,000 rifles total. The army liked these because being single shot they didn't expend ammo so rapidly as the Henry, and they fired much more powerful cartridges. The most successful lever rifle of the civil war in terms of number acquired was the Spencer rifle, which had a tube magazine in the buttstock. These were acquired later in the war when the union army was getting its ammunition supply issues under control. Still, only a few were issued to infantry. Most went to cavalry units, since the cost of supplying horses was already so high it made sense to maximize the firepower of each cavalry trooper with a repeating rifle. About 110,000 were acquired during the war, most in the shorter carbine length preferred by cavalry. The army preferred Spencers to Henrys because they fired a somewhat more powerful, longer range cartridge and the Spencer was easier to reload on horseback.

After the civil war was over the victorious U.S. army went into an economizing mode. The army saw the value in breech loading rifles, but was wary of magazine repeaters due to the high ammunition expenditure. The army ultimately decided to avoid the expense of adopting a new rifle and instead decided to modify its large existing stock of muzzle loading 1861 Springfields to breech loading, and this process resulted in the single shot "trapdoor" Springfield becoming the new standard rifle in 1873. The converted rifles had neither levers nor bolts, loading via a hinged breechblock dubbed the trapdoor. The army units equipped with Spencers or other weapons leftover from the civil war were required to exchange them for the converted Springfields, which resulted in many complaints, but the army turned a deaf ear.

The U.S. army occasionally tested new rifles over the next 20 years, but repeatedly concluded that their existing trapdoor Springfields made more economic sense than any alternative.

Change would come in 1892, not because the army really wanted a magazine rifle, but because smokeless powder had been invented. Smokeless powder offered the considerable advantages of more powerful cartridges, greatly reduced smoke blocking the soldier's vision and revealing his position, and less fouling of the rifle barrel from powder residue.

The army held trials of no less than 53 rifles submitted for competition in 1892. Of those, rather oddly in hindsight, nearly all were bolt actions. A new company called Savage entered a prototype lever gun, but they had no previous track record or production facilities and were not really taken seriously. It is unclear to me whether the Winchester company, the most famous manufacturer of lever guns in the world, even entered the competition; anyone who can shed light on this please contact me or comment. Winchester at this time had not yet developed a smokeless cartridge or a rifle that used one, so any weapon they may have offered was quickly rejected by the army.

To everyone's considerable surprise and much comment, the weapon the army ultimately settled on was a Norwegian designed rifle, the Krag-Jorgensen. The Krag, as it became known, was a magazine fed bolt action. Tellingly, the new rifle's rate of fire was somewhat limited by not being suitable for loading with stripper clips like several competing designs. The Krag also had a feature called the magazine cut-off; when engaged the cut-off prevented the rifle from loading from its magazine and turned it into a single shot weapon. This allowed officers to limit "wasteful" rapid fire.

The next development in this story is the coming of the Spanish-American war (1898). The most talked about land engagement of the war was the famous charge up San Juan hill in Cuba, which included the participation of Theodore Roosevelt and his famous "Rough Riders". This was initially lauded as a heroic success, but a critical analysis revealed disquieting details. The battle was rather numerically lopsided, with some 7,000 American troops attacking 750 Spanish defenders. Somehow the badly outnumbered defenders had inflicted 1,400 casualties on the Americans. It turned out the Spanish had better rifles. Their 7mm Mauser rifles loaded faster and had longer range than the American Krag. Actually, many of the American troops at San Juan, perhaps over half, were equipped with old trapdoor Springfields firing black powder cartridges. But the message the public understood was that the army's new Krags were inferior to enemy Mausers. And no one was more infuriated by this deficiency than Theodore Roosevelt.

When Roosevelt was elected vice president in 1900, he worked to modernize the armed forces, particularly the army, with president McKinley's approval. After McKinley's assassination and Roosevelt's ascendance to the presidency, this modernization continued more rapidly. Newly appointed officials in the army were ordered to develop a new rifle for the army equal to the Mauser in capability. A series of improvements were introduced to the Krag design to increase its capabilities. Several intermediate prototypes were developed, and in 1903 this process was essentially complete, resulting in a new rifle that became known as the 1903 Springfield. Perhaps not surprisingly, given the rigid requirements of matching the Mauser's capabilities that Roosevelt insisted on, the new rifle looked and worked a lot more like a Mauser than a Krag. So much so that the U.S. government would eventually have to make substantial royalty payments to holders of patents on the Mauser and it's ammunition.

It's a bit odd that the army doesn't seem to have seriously considered adopting a lever gun to replace the Krag. By this time the 1894 and 1895 Winchester rifles were available, both with strong actions capable of firing the latest smokeless powder cartridges, and the 1895 had a box style magazine like the Mauser. Savage had also improved its 1892 lever action prototype and was now selling small numbers on the commercial market. But it seems the procurement process was driven by Roosevelt, who had become a zealous fan of the Mauser as a military rifle, even though he had himself used and praised Winchester lever guns as hunting weapons. It does seem there was an element of pride involved in the army producing its own design rather than acquiring a license to a civilian weapon. The army carefully ignored the fact that the 1903 Springfield, despite it's roots as an evolved Krag, was really a Mauser clone.

In world war 1 there weren't enough 1903 Springfields to go around and the army wound up acquiring large numbers of a rifle that became known as the 1917 Enfield, mostly because they could be introduced and acquired quickly by using factories that were already building rifles for the British. All that was needed was to retool the chambering of the British rifles to accept the American 30-06 cartridge. The U.S. army rejected the possibility of acquiring Winchester lever guns to fill the gap because the Enfields could be produced in greater numbers and they were outwardly similar to the standard Springfields, simplifying training.

Finally the whole lever vs bolt question, to the extent it ever existed, was rendered moot when the army adopted the self loading M1 Garand rifle in 1936.

There are objective reasons for preferring bolt actions for military use over lever actions. As u/PartyMoses has pointed out, the lever guns were somewhat more complex, which in turn also made them somewhat more expensive and was thought to make them more likely to malfunction. There was also a complaint that it was difficult to work the action of a lever gun by a soldier in the prone position. But none of that was really relevant to the U.S. army's decision to acquire bolt action rifles starting in 1892. The big driver to adopting a new rifle at the 1892 trials was the desire to put powerful smokeless powder rifles into service, and no lever gun capable of firing those cartridges was in production. The Savage 1892 prototype mentioned above apparently was chambered for the .30-40 smokeless cartridge the army adopted for the Krag, but the Savage prototypes were not as well developed as the famous Winchester designs and had no track record to recommend them. The adoption of the 1903 Springfield that replaced the Krag was driven by a desire to match the Mauser, and since the Mauser was a bolt gun so was the gun the army developed to match it. The army was very happy with the 1903 Springfield and had no interest in replacing it until the self loading Garand design was perfected.

In writing this I have referred to the book American Rifle: a biography, by Alexander Rose. I have also referred to various Internet resources; I particularly recommend Ian McCollum's YouTube channel Forgotten Weapons and it's associated web site.

While you would be correct in assuming that lever actions were not as popular there are a few interesting cases of lever action rifles being put into military service. I was also curious so I went ahead and did some reading into the topic, I found that the Winchester Model 1895 did see limited service in the Imperial Russian army, within the Ottoman Empire and within the British Army during WW1 (More on its applications withing the First World War later in the explanation). As far back as the Russo-Turkish (1877-78) the Ottomans used the Winchester Model 1866 and were said to have decimated Russian troops in some engagements due to superior rates of fire. Around the turn of the century the Russians bought significant numbers of the model 1895 and were issued to units in their western frontiers in the Baltics and Finland. They feasibly could have been used during WW1. Interestingly they were chambered in 7.62 and came patterned with a bayonet lug. Some of these rifles were later sold to Spanish revolutionaries by Stalin in the 1930's. Limited numbers of the Model 1895 were patterned for the British Army during WW1 to fire incendiary ammunition designed to destroy German Zeppelins.

https://www.americanrifleman.org/articles/2015/6/11/winchester-lever-actions-go-to-war/ http://www.winchesterguns.com/news/articles/150-years-of-winchester-winchester-goes-to-war.html