The text for Smite Evil says - The smite evil effect remains until the target of the smite is dead or the next time the paladin rests and regains her uses of this ability. At 4th level, and at every three levels thereafter, the paladin may smite evil one additional time per day, as indicated on Table: Paladin, to a maximum of seven times per day at 19th level.
So, that means one use of Smite per target, correct? The paladin keeps getting bonuses against the evil opponent as long as it's alive, and that's just one use of Smite.
Ok, thank you.