Glen Elendra Archmage

If a creature with persist that has +1/+1 counters on it receives enough -1/-1 counters to cause it to be destroyed by lethal damage or put into its owner's graveyard for having 0 or less toughness, persist won't trigger and the card won't return to the battlefield. That's because persist checks the creature's existence just before it leaves the battlefield, and it still has all those counters on it at that point.

If multiple creatures with persist are put into the graveyard at the same time (due to combat damage or a spell that destroys all creatures, for example), the active player (the player whose turn it is) puts all of their persist triggers on the stack in any order, then each other player in turn order does the same. The last trigger put on the stack is the first one that resolves. That means that in a two-player game, the nonactive player's persist creatures will return to the battlefield first, then the active player's persist creatures do the same. The creatures return to the battlefield one at a time.

If a token with no -1/-1 counters on it has persist, the ability will trigger when the token is put into the graveyard. However, the token will cease to exist and can't return to the battlefield.