Removing persist from a creature -- will it still trigger?
702.78a Persist is a triggered ability. “Persist” means “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.”


Key here is "triggered ability", which happen as the event occurs.


  603.2. Whenever a game event or game state matches a triggered ability’s trigger event, that ability automatically triggers. 


At the time the event happens, the permanent doesn't have Persist, so nothing triggers. It's only after the event concludes that Persist returns to the card.