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Why did Yamamoto declare Operation I over in April 1943?

Short answer

Because he believed it had been a success: he thought Allied losses were greater than they actually were. He ended it on 16 April, and Japanese carrier aircraft returned to their ships. Japanese reports claimed 175 aircraft shot down and 28 ships sunk; in reality it was up to 25 aircraft and five ships.

Why did Yamamoto declare Operation I over in April 1943?
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An offensive to buy time

Operation I-Go sought to halt the Allied offensives to give Japan time to prepare a new set of defences, in response to recent defeats.

An inflated tally

Japanese claims totalled 175 aircraft shot down and 28 ships sunk, including a cruiser and two destroyers. In reality, total Allied losses during the operation were five ships of various types and up to 25 aircraft. The Japanese, for their part, lost 55 aircraft destroyed.

The end of the operation and what followed

Yamamoto declared the operation over on 16 April. At the time he believed Allied losses had been more severe than they actually were and that the operation had been a success, and Japanese carrier aircraft then returned to their ships. After the operation, Yamamoto decided to travel to the Solomons to congratulate his air crews. On 18 April he died when the aircraft he was flying in was intercepted and shot down during Operation Vengeance.

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Why did Yamamoto declare Operation I over in April 1943?