The Soulsavers are immortal, and like Tavrobel said, are there to prevent the battle from ending. (And you can X-Zone them, of course).

When Wrexsoul disappears, he's possessing one of your characters. This isn't made very apparent from the game, giving frustration to a 10-year old me. You actually have to hurt your own party members (to just critical health? I always thought you have to kill them off, but meh) to make him reappear, then you attack him again.

It's much easier to Vanish/X-Zone though.