It depends on what type you are playing. In Type 1, you don't attack for a specific Lost Soul, so any Soul your heroes have access to can be rescued until the end of battle. If your opponent shuffles/discards/places under deck all Lost Souls your heroes have access to, then your RA becomes a BC.
In Type 2, you DO attack for a specific Soul that you announce at the beginning of the rescue. For the remainder of the RA, your heroes ONLY have access to that Soul, if that Soul is shuffled/discarded/placed under deck, then the RA becomes a BC. In either case, the battle continues as a battle challenge, and characters only return to territories if both players agree to end the battle challenge.
