Gravelgill Axeshark

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 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.

If a permanent has multiple instances of persist, they’ll each trigger separately, but the redundant instances will have no effect. If one instance returns the card to the battlefield, the next to resolve will do nothing.