Death could work as a god as I'm fairly sure that Death has been personified as a being and just simply called Death. Don't play Death the concept, play Death the mythological personification. That way it is perfectly reasonable for people to lose faith in such a god over time. I believe in death, of course, but I don't believe in some sentient being that comes to drain the life force of the living when it is their "time". The thing here is that people used to believe that death was actually caused by an entity, which is what your character is.

You could put some kind of limitation on this power, like, I don't know, maybe your char doesn't actually control it, maybe it only happens if it's the person's "time" to die. In European mythology, Death only comes when fate dictates that someone must die. Here's the wiki page that talks about Death as a mythological figure, which also talks about how Death is portrayed in various parts of the world:

Death (personification) - Wikipedia, the free encyclopedia

As far as god-moding goes, my character Gabriel's power is almost the opposite of yours, (although I don't think it goes as far as resurrecting people from the dead) and has the potential to be nearly limitless, however he's fairly confused about what's happening to him at the moment.