Persist (CR 702.79a) 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 condition is no -1/-1 counters at the time it left the battlefield.
When determining whether persist triggers, the game uses the 'last known information' about the permanent as it existed on the battlefield just before it moved to the graveyard (CR 603.10). If the creature had even a single -1/-1 counter on it at that moment, the persist ability's condition is not met and the trigger simply does not occur.
Sacrificing the creature is irrelevant to this check — whether it died by sacrifice, combat damage, or a destroy effect, what matters is the presence or absence of -1/-1 counters on it right before it left play.
Concrete example: You control a Murderous Redcap (which has persist). It has already returned once via persist and thus carries a -1/-1 counter. If you sacrifice it (say, to an Altar's Reap), its persist ability does NOT trigger because it had a -1/-1 counter on it. It stays in the graveyard.
If, however, the -1/-1 counter had been removed before it died (e.g., through a counter-removal effect), then persist would trigger normally and return it with a fresh -1/-1 counter.
Unofficial fan resource — not affiliated with or endorsed by Wizards of the Coast. Answers are AI-generated estimates grounded in the Comprehensive Rules and are not a substitute for an official judge. Verify anything match-critical.