Immortal units also have a chance to lose an affliction when they come back to life. I don't have the % for that in front of me, or I'd let you know what it is. I *think* it is a pretty good chance, but I'm drawing a blank.
I remember a game where my Bog Mummy pretender had gotten the Mute affliction, which did not do wonders for his magical abilities. I deliberately sent him off to get killed. He picked up a Limp in that battle, but came back without Mute. For a unit who is just meant to stay in back and cast spells, trading Mute for Limp isn't bad at all.