He recovers at the speed of plot!
I think it's weird that on the show he's portrayed taking hours or days to recover; in every other portrayal his recovery is pretty immediate. Also, elsewhere he only seems to lose his invulnerability and strength, not his other powers, under the influence of Kryptonite, which is more the way he's portrayed in Madam Ex, where he can still use his heat vision while he has a bullet in his shoulder.
It seems to me that I've read stories that address this in passing, but I can't remember anything specific.
