There are a couple of facets to the answer, and frankly a lot of it is guesswork. Sulla was a very complex personality anyway, and the records got so muddied both during his lifetime with the propaganda from Marius and Sulla himself, and the later factions that biased one way or another; Sulla's position as the first man to march on Rome meant that it was often a source's position on that event which dictated how they saw Sulla himself, which doesn't lend itself to unbiased sources coming down to us.
He wanted to be as constitutional as possible, and keep the position of Dictator for as short a time as possible. Sulla always stressed the legality (within the Roman mos maiorum) of everything he did, and always claimed his march on Rome was to restore legality and order. Obviously we don't really have any idea of how much of this is propaganda from Sulla himself, but his laying down the position of Dictator does suggest that this view has a certain validity.
Following on from this...that was what was done. The position of Dictator was only held in times of crisis; once the crisis was fixed, that was it. Romans only held ultimate power (either consulship or proconsul, or obviously dictator) for short periods of time. Even though Sulla had done the unthinkable and marched on Rome, he still very much saw himself as a Roman, and Rome had no place for a permanent dictator in its political mindset (at that stage, at least).
He felt he had done everything required. He has restored Rome, restored the balance of power, returned the Senate to what he felt was its rightful position...he had also ensured that no one would ever gain the same power to destabilise Rome (primarily by stripping the tribunate and Plebs of power) and therefore everything was right again. The laws and checks/balances would do their job, and Rome could return to normal political life.
He may have known that he was dying; he likely knew that he was ill - he wrote his memoirs shortly after he stepped down. The illness may have influenced how long he felt he had left, and what he wanted to do with the time.
I also wonder (and this is pure speculation) if he felt that he needed to 'let himself go' after completing his duty, and return to his old lifestyle - if he remained as dictator when he didn't feel it was needed, he wouldn't have been able to have some fun again before he died.
In summary: the position of dictator wasn't needed, the Republic was restored, and so he stepped down. He saw no need to remain in power - in obvious contrast to Gaius Julius Caesar, a generation later.
Sources: "Sulla, The Last Republican" by Arthur Keaveney is a very good look at Sulla specifically, and Scullard's "From The Gracchi To Nero" has a good section on the political implications and events. Beyond that, unfortunately Sulla isn't particularly well covered and tends to get overshadowed by the man who didn't step down, Caesar. I've found that Colleen McCullough's "First Man In Rome" series has some interesting speculations, although it is historical fiction and so must be treated with caution.