All state-based actions are checked at the same time, not one at a time. After the Command is done resolving, we have two state-based actions that want to apply: the game wants the Finks to go to the graveyard since it has lethal damage marked on it, and the game wants to remove the +1/+1 and the -1/-1 counter from the Finks, and both happen at the same time. Since there's never a point where the Finks is on the battlefield and it doesn't have a -1/-1 counter on it, persist will not trigger for the Finks.
Nathan Long
Wizards.Com Boards NetRep