If a creature with persist dies and returns, then later dies again, does persist trigger a second time?

Persist (CR 702.79) states: 'When this permanent is put into a graveyard from the battlefield, if it had no -1/-1 counters on it, return it to the battlefield under its owner's control with a -1/-1 counter on it.' The critical phrase is if it had no -1/-1 counters on it.

When a creature with persist dies and returns via persist, it comes back with exactly one -1/-1 counter on it. If that creature then dies a second time, persist checks whether it had no -1/-1 counters when it left the battlefield. Since it still has at least that one -1/-1 counter, the condition is not met, and persist does not trigger again.

The only way persist can trigger a second time on the same creature is if all -1/-1 counters are removed before it dies again — for example, by using an effect that removes counters or by having a +1/+1 counter cancel out the -1/-1 counter (CR 121.3, counter cancellation rule).

Example: Woodfall Primus (a creature with persist) dies, returns with a -1/-1 counter. Your opponent then kills it again. Because it has a -1/-1 counter on it when it dies, persist's condition fails and it stays in the graveyard.

However, if before that second death you had given Woodfall Primus a +1/+1 counter (canceling the -1/-1 counter via CR 121.3), it would have no -1/-1 counters when it dies, and persist would trigger again.