Pokémon's sleep counter should save even when switching out and then in

[varkor]

This change was made in Gen. VI. However, if you enter a new battle, it will reset.

[fuzzball288]

Adding onto this, how sleep works:

Pokemon stay asleep for 1-3 moves. Each time a Pokemon tries to move, it counts as a "turn" of sleep.

If a Pokemon moves first, then is put to sleep by the opponent, that doesn't count as a sleep turn. The next turn, when it tries to move, it will count as burning a turn of sleep. If a Pokemon is put to sleep by something faster than it, that same turn counts as burning the first turn of sleep, and it may wake up at the start of the next turn.