I disagree with the good Professor. Unless negated, or they state otherwise, all abilities last until the end of the phase. Therefore the Pigs Lost Soul would continue to be active for the rest of the phase in which it is rescued, unless it was negated first.
Contrast Pigs with Speed Bump for example, "While this card is in play, protect all Lost Souls from rescue by a player with more than 10 cards in hand."
Speed Bump is no longer active after it leaves play because of the clause in it's SA.