The main source for these claims of a lost opportunity are the Pacific Fleet commanders Admiral Husband E. Kimmel and Chester Nimitz. In Gordon Prange's monumental works on Pearl Harbor, At Dawn We Slept and Pearl Harbor: The Verdict of History, Prange recapitulated both officers' claims that the Japanese missed a plum opportunity to attack these facilities. Nimitz framed the lost opportunity thus:

We had about 4.5 million barrels of oil out there and all of it was vulnerable to .50-caliber bullets. Had the Japanese destroyed the oil, it would have prolonged the war another two years.

Kimmel would likewise claim that attacking the oil tanks would have forced a full retreat from Hawaii to the West Coast. These claims, coming from very highly placed USN sources, have led a number of popular authors like Daniel Yergin to repeat them verbatim. The problem is that both Nimitz and Kimmler were speculating on a hypothetical attack and its maximum carnage. However, the oil reserves were a much harder target for the Japanese to destroy than either Nimitz or Kimmel suggest.

Nimitz's claim that a .50-caliber bullet could have allowed these tanks to go up in flames is faulty on two grounds. One, Japanese aircraft attacking Pearl had only 7.7 mm machine guns as their main armament. Fragments of 7.7 mm shells could have penetrated the the tops of the oil tanks, but likely would not have the mass to ignite the fuel vapors inside them. The 20-mm cannon of the A6M2s might have caused ignition, but the Zeroes carried a limited amount of the shells. Neither gun could have penetrated the ca. 1 inch steel sides of the tanks, so a strafing attack would have been quite difficult. So far from a cheap destruction via strafing, the best that the Japanese could have hoped for was holing a few tanks and perhaps setting one or two on fire.

So in this case, to destroy the oil tanks would require detailing bombers to attack the facilities. The Japanese air strikes were predicated upon a tight parceling out of the available strike aircraft, so to attack the oil fields, the Japanese planners would have had to abandon attacking other targets like the battleline or Oahu's airfields. Such a dispersal might have paid long-term dividends, but it would have allowed the USN to stage an immediate counterattack with existing reserves. Nor could Kido Butai have conducted a third strike against Pearl's facilities. Shortcomings in Japanese munitions production meant that the Pearl Harbor strikeforce only had the minimum munitions to conduct the airstrike and maintain a reserve of bombs and torpedoes for contingencies. Moreover, the refueling of both Kido Butais escorts and carriers was dependent upon a complex series of rendezvouses with tankers. The Japanese carriers could not loiter in Hawaiian waters for another strike. Antony Tully and Jonathan Parshall have noted that the idea of a Nagumo-vetoed third strike, immortalized in films like Tora, Tora, Tora and Pearl Harbor, was largely a postwar construction that did not appear in the immediate postwar debriefings of Genda or Fuchida.

The idea of a massive fire and complete destruction of the oil reserves is a bit of a stretch given the experience of other wartime raids like the ETO's use of heavy four-engined bombers or the Luftwaffe's belated Caucasus oil campaign when Stalingrad bogged down showed that destruction required greater tonnage of bombs than the B5Ns and D3As could carry. But assuming for sake of argument that the Japanese could have set fire and destroyed Pearl's oil reserves, the result would have been detrimental to the USN, but not the two year delay Nimitz asserted. The US had ample tankerage which could have met the needs of the Pacific fleet in harbor while the Red Hill Underground Fuel Storage Facility was constructed. Counter-intuitively, shifting more tanker assets to the Pacific might have helped the American war effort. Germany's entry into the war and the inexperience and stretched ASW assets on the Atlantic meant that US tankers were the victims of the German U-boats' second "happy time." Tankers were among the U-boats' favorite targets in this period. IJN submarines were much less effective at seaborne interdiction than their German allies, and shifting Atlantic tankers to the Pacific would have prevented some of these tankers from being sunk.

Make no mistake, a destruction of the oil tanks would have hindered the American war effort. it would have been a psychological blow and likely injected more caution in USN responses to Japan. American admirals would have had to operate with the knowledge they were at the end of more tenuous logistical tether in such a scenario. The US responded to Operation MO (the Battle of the Coral Sea) thinking they were facing three fleet carriers, not two, and this shows the type of recklessness that lack of fuel might have put a damper upon. But this would not have been a war-winning option for Japan, even if an attack had gone perfectly correct and destroyed the reserves. In hindsight, it is easy to fault Japan for attacking X when they could have gone with Y. For example, had the air strikes focused on smaller escort ships at Pearl, they could have hamstrung USN operations and inflicted a more permanent loss on the fleet. Smaller ships like cruisers or destroyers may have been damaged permanently by Japanese aircraft and the personnel losses from these less armored ships would have been higher. The personnel shortage of the expanding USN was acute in 1941/42 was quite acute, and even after the losses from the battlewagons were taken into account, the personnel from the sunk and disabled battleships filled in a niche that the USN needed to fill. Naturally, structuring the attack to harm the personnel structure would have required intelligence knowledge on the USN that no military in 1941 could have conceivably possessed. With the resources the Japanese had in 1941, the results of the Pearl Harbor attack was arguably as good as they realistically could have been.

Sources

Parshall, Jonathan B., and Anthony P. Tully. Shattered Sword: The Untold Story of the Battle of Midway. Washington, D.C.: Potomac Books, 2005.

Willmott, H. P., Haruo Tohmatsu, and W. Spencer Johnson. Pearl Harbor. London: Cassell, 2001.

Zimm, Alan D. Attack on Pearl Harbor: Strategy, Combat, Myths, Deceptions. Philadelphia [Pa.]: Casemate, 2011.

I would actually contend that it would have had a lessor impact than might have been imagined. And that it became a trope for a few congruent reasons.

1. We should consider the nature of the tanks and their contents. The tank farm was easy to spot, but not as vulnerable as might be considered. The tanks themselves were reinforced to the point that really only a direct hit would do, while the pipe infrastructure and connections out to ships were also protected with much of it being underground. aerial shot of the tank farm.

2. While there really wasn't much activity in the first 2-3 months for the IJN to restrict by taking away a few of the tanks. The abortive Wake Island relief might still have gone through as that was really Kimmel's long shot to try to salvage something from the opening of the war. But other than that the carriers mostly stay near to Oahu save for the Feb 1 raids on the mandates and follow on attacks by the Enterprise on Wake. While the Saratoga caught a fish from an I Boat and had to go for repairs, and the Enterprise was joined by the Yorktown from California. Lexington then was sent to the South Pacific where her task force would have to get fuel from tankers and sources not reliant on Pearl.

   Thus it was only months later when the operational tempo accelerated with the Hornet's arrival and the start of the Doolittle Raid. While Yorktown shifted south as well in the lead up to the battle of the Coral Sea. So simply put there was only a marginal at most and optional usage of fuel for weeks after Pearl Harbor, and California was the ultimate source of fuel for half the fleet's carriers come Spring when they shifted to the South Pacific.

3. That the AO's, or Oilers, were the far more restrictive part of the fueling pipeline for the fleet. The USN was acutely aware that it was too reliant on older slower WW1 vintage oilers to support fleet. Many of these ships were too small to fuel an entire task force, and could barely make 12 knots. The naval buildup did include larger and more modern ships but like everything about the Navy in 1941 it was a work in progress. For instance had the Neosho, or Ramapo in port during the attack been sunk, or the Platte with Halsey been caught that would have greatly restricted the ability of task forces to operate at any distance from home with any number of destroyers.

4. Is finally the type of fuel stored in them. The Avgas or aviation gas tanks around would have gone up in a nice big explosion. But those were a minority of the fuel there. Most of it was for the ships, and known as Bunker Fuel. And honestly its more like a sludge than a liquid, it actually has to be heated up before being burned as fuel. And that means it is both easier to produce(and cheaper), and more stable. I honestly can't think of a time that a shipboard explosion was the result of Bunker Fuel being ignited.

Now as you your actual question about why they were not attacked. Its actually quite simple. They were far down on the target list for the Kido Butai. The goal was to knock the Pacific Fleet badly off its footing immediately to buy operational freedom, not to restrict its movements a month from then. That goal then was best achieved by attacking the ships themselves. Even in an event of a hypothetical improvised 3rd wave, which Nagumo was wise to not order, it is unlikely that much damage might have been done. To say nothing of the immense challenges with even loitering for another 24 hours that the KB faced. Fuchida, master of the truth that he is, supposedly suggested that focus, as did some other officers, while Yamaguchi supported seeking out undamaged ships, including the Enterprise thought to be lurking about. So while a 3rd wave might have seen a few bombs thrown towards the tank farm again, and Dry Dock 1, and the HQ building possibly. It would have been in the late afternoon, with tired pilots, in the face of a fully alert defense from the ground. Not a recipe for success, or at least the level of success that would cripple a fleet.