The target would disappear from sensors so the missile would go into auto-search mode (or self-destruct if it lacks on board sensors).
Thanks, make sense. Though I would support missiles without sensors switching to the carrier, as serger suggests. If the previous target reappears (the fighter is again launched) should the missile switch back again?
If the missiles have any sensors chance is they lock on the carrier next as carriers are usually quite big. Hmm, though that probably depends on the type of sensors they use, say, for thermals there may be other ships with strong engines in sight.