You could lose all of your believers, for example. Or a more powerful god, or a demon, or a ghost can kill you. Or you can be banished from heaven, although that doesn't necessarily make you not immortal anymore, you just can't go back.

... That's just where I'm from, though. Most people I have talked to, apparently their gods are immortal for good not just for as long as they can maintain it. We call that 'immortal' because it's easier as a concept.