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Relevant rule from the Bloody Vengeance feat:
Benefit: If an opponent within line of sight has damaged you within the last minute, you may study that opponent as a standard action. Thereafter, if you hit that opponent with a melee attack, you deal 1 point of bleed damage to that creature in addition to the normal damage dealt by your attack.
"Thereafter" is a heck of a word. I presume its use here effectively means "before the end of that same encounter".
What's less clear is whether or not the ability to cause bleed damage expires after the first hit, or if it too lasts the full duration of "thereafter". Again, presumably no longer than the end of the encounter (in the event that target manages to escape alive)