Leonard’s condition isn’t physical, but rather psychological, much like he says in his fictionalized version of the Sammy Jankis case (That’s really what happened to him, not Sammy). All of the quick cuts you see in the final 5–10 minutes (including the quick shot of him in the institution, and the “I’ve done it” tattoo on his chest.) Is just his brain blocking out what, deep down, it already knows.
Example: Teddy tells him it was his wife that had diabetes. Then we get a quick cut of him giving his wife an insulin shot. Then Leonard claims “my wife wasn’t diabetic”, which is followed by another quick cut exactly like the last except he’s not administering insulin, but rather just pinching her hip. That’s his brain “Conditioning itself”.
This of course is just my opinion on the movie (one of my all-time favorites), and Teddy could totally just be full of shit.