Dive bombers were used repeatedly, and effectively, after Midway, and up until 1945 in the USN. At the Battle of the Eastern Solomons, American dive bombers sank the light carrier Ryujo, while Japanese ones heavily damaged the USS Enterprise. At Santa Cruz, American dive bombers heavily damaged Zuiho and Shokaku, as well as the cruiser Chikuma. Dive bombers were present at Leyte Gulf, and were useful in reducing and destroying ground targets during preliminary bombardments for island landings. They were also used in Europe. The Fairey Barracuda, a torpedo bomber that could also dive-bomb, was used repeatedly against the Tirpitz by the RN. While these raids weren't the most successful, they did cause major damage to Tirpitz. German and Italian dive bombers (including the Stuka, but mainly the Ju-88) were a persistent threat to Allied shipping in the Mediterranean until the Allied landings in Italy forced their bases away from the major shipping routes. The increasing accuracy and effectiveness of guided weapons did cause the dive bomber to become obsolete as the war ended, but it was still useful right up until the end of the war.

However, in none of these cases were they as effective as they were at Midway. This isn't especially due to any change in usage or due to a lack of targets, but simply because they were almost unreasonably effective at Midway. To see this, we can compare Midway to several other battles in which dive bombers took part. At Midway, Akagi was reduced to a burning hulk by a single 1000 lb bomb. Kaga was hit by three 500lb bombs and one 1000 lb. Soryu was hit by three bombs, one of which was a 1000 lber. However, if we compare this to other battles, it can be seen how unlikely this was. At Coral Sea, Shokaku was hit by three bombs, but survived to take four to six 1000 lb bombs at Eastern Solomons. If we take Midway as a guide, we'd have expected her to sink at both battles, but instead she survived until torpedoed by a submarine at the Philippine Sea. She survived both battles because her hangars were empty. At Midway, the carriers had their full strike wings in their hangars, loading ammunition and refueling for a strike on the American force, while at both battles Shokaku was attacked after launching her strike force. While bombs could penetrate her flight deck, and cause fires as they did at Coral Sea, there was not enough fuel present to turn the fires into the sort of fore-to-aft infernos seen at Midway. Additionally, there was no ammunition present to cause devastating secondary explosions. However, the presence of aircraft in the hangars was not solely the cause of the effectiveness of the dive bombers at Midway. On the 10th January 1941, the British carrier HMS Illustrious was attacked by German and Italian dive bombers in the Mediterranean. She took six direct hits, five from 500 kg (1100 lb) bombs and one from a 1000 kg (2200 lb) bomb, but managed to make it to Malta, where she was repaired. She had nine fuelled and armed Swordfish attack aircraft in her hangar, and six torpedoes stored in readiness for an attack. Part of the reason she survived was due solely to luck - 3 of the 500kg bombs hit her after lift well, rather than penetrating through to her hangar deck, while the other two penetrated the flight deck, but did not enter the hangar. The 1000kg bomb penetrated the after part of her hangar; while the armed aircraft were further forward, it did start a major fire in her hangar. However, unlike the Japanese carriers at Midway, she had multiple redundancies in her fire control systems, and a crew that was well trained in damage control. Illustrious's sprinkler system was divided into three separate systems, A, B and C, depending on the part of the hangar it covered. The aft-most system, C, was mostly destroyed by the bombing, but the two forward systems were still operational, and prevented the fire spreading forwards. In addition, the systems had a port/starboard split, ideally preventing a single bomb destroying a single system in its entirety. The carriers at Midway had only a single sprinkler main, easily destroyed by the bomb blasts, and leaving them unprotected against fire. Her crew was all well trained in damage control, allowing the fires to be effectively controlled despite losses to her crew. On the Japanese carriers, there were only a few crew well trained in damage control. When they were killed by the fire, there was nobody who could effectively fight it. The British carriers Formidable and Indomitable would also take bomb hits in the Mediterranean, but because the British design had the hangar surrounded by workshops and accommodation spaces, no major hangar fire resulted. On American carriers, if a hangar fire occurred, the open hangar design allowed escort ships to come alongside, and help fight the fire. The Japanese design had neither of these advantages. Midway was a perfect storm for the dive bombers - all of these weaknesses came together to make the Japanese carriers a perfect target. This would not happen again.

Sources:

Shattered Sword, Jonathan Parshall, Anthony Tully, Potomac, 2008

www.combinedfleet.com

British Carrier Aviation: The Evolution of the Ships and Their Aircraft, Norman Friedman, Naval Institute Press, 1988

H. M. SHIPS DAMAGED OR SUNK BY ENEMY ACTION 3rd. SEPT. 1939 to 2nd. SEPT. 1945, C.B. 4273(52), Admiralty, 1952

HMS Illustrious Bomb Damage Report, ADM267/83, C. S. Lillicrap, 1942, found at (http://www.armouredcarriers.com/adm26783/2014/10/16/illustrious-january-10-damage-report-bomb-shell)

Nelson to Vanguard: Warship Design and Development 1923-1945, D. K. Brown, Seaforth, 2012

Well, it's not as simple as "dive bombers won Midway."

Just before 9:30 AM on June 4, 1942, approximately 150 American dive bombers and torpedo bombers from Hornet and Enterprise had located the four Japanese carriers. The first aircraft were spotted on approach and within just six minutes, every one of Hornet's torpedo bombers was shot down by Zeros, and Enterprise's squadrons lost ten torpedo bombers. The dive bombers lost track of the carriers due to a course change by the Japanese fleet, and were forced to ditch, return to their home carriers, or land at Midway. All of the fighter escorts ditched when they ran out of fuel.

However, Yorktown had launched her squadrons an hour after Hornet and Enterprise, and her pilots located the Japanese carriers by following the plumes of smoke generated in the recent combat. The torpedo bombers were again almost totally destroyed by the Zero escorts, and the Japanese fleet had yet to sustain damage.

The thing about torpedo bombers, though, is they attack from a very low altitude. So, the defensive screen of Zeros were at a very low altitude.

It was at this point, 10:25 AM, that a group of Dauntless dive bombers commanded by Lt. Com. Wade McClusky, having spent more than an hour completely lost over the ocean, spotted the Japanese fleet below them. Almost simultaneously, the dive bombers from Yorktown arrived.

From 14,500 feet of altitude, with nothing but open air between them and the carriers, forty-seven dive bombers from Enterprise and Yorktown attacked the Kaga, Soryu, and the flagship, Akagi. The Japanese carriers' flight decks were covered with ordnance for rearming their planes, and fuel hoses for refueling them.

In less than five minutes, by 10:30 AM, all three carriers were death traps, ablaze and in serious trouble. By 5:00 PM, Enterprise's surviving dive bombers had located Hiryu, the surviving carrier, and forced her crew to scuttle her.

Dive bombers were not a trump card. At Midway, they succeeded with skill, intelligence, a hell of a lot of very good luck, and, most of all, the sacrifice of hundreds of brave aviators in the fighter escorts and torpedo bombers.

Dive bombers continued to be deployed to great effect in every theater, but their failure to chalk up a string of successes similar to Midway is due simply to the fact that their five minutes of glory at Midway was "the most stunning and decisive blow in the history of naval warfare." Midway was a greater victory than Trafalgar or St. Vincent or Actium or Salamis.

So yeah, dive bombers didn't perform any more miracles.

Further reading: John Keegan, World War Two, chapter fourteen

Edit: mistyped a couple things. Swype ain't perfect

I would say you might not be looking very close.

In the last two carrier battles of 1942 for instance the Bombing and Scouting squadrons which were equipped with DBs were the primary parts of the strikes. At Eastern Solomons they got thr Ryujo and yhe Zuikaku at Santa Cruz. As well as Navy and Marine DBs serving with distinction in the CACTUS Air Force on Guadalcanal.

However all through the run up to war and on both the US and IJN viewed the Torpedo Bomber as the more powerful strike weapon as a single fish could do much more damage than a single bomb.

However some unfortunate conclusions on the US side led to the situation at Midway you mention. At Coral Sea the DB attacks arrived first and mostly without fighter escort and ran into CAP fighters before pushing over. The result was a call for more escorts for them up high. Meanwhile the TBs faired relatively well and it was concluded that a close escort was less crucial. While early war not enough fighters were carried to escort both and provide CAP. By Guadalcanal that was mostly resolved.

So at Midway outside of a handful of fighters, notably Thatch's flight, were on close TB escort. Contributing to the slaughter. Along with the fact that outside Torpedo 8 no other Hornet aircraft engaged because of poor navigation by the CAG.

So then of course any damage done then would be from the DBs. Though it should be noted over a dozen TBs did manage to release their fish though all either missed or were duds though some hits were claimed at the time.

The IJN always were better about coordinated cross type attacks and the 3 big carriers( Lexington, Yorktown, and Wasp) they sank in 42 in battle all reflect that.

I have to note as well that dive bombers were much less effective against armored targets such as battleships; and the Japanese had reverted to using battleships as their primary striking force by Oct 1944 onwards after their carriers had run out of pilots.

I see a lot of comments about how effective dive bombers were at Midway and other battles, but nobody has answered the question about why we stopped using them.