I'm fine with a bleak story as long as there's a point to it. Things that just keep getting darker and darker and darker just for the sake of being dark bore me; if it's clear that nothing matters and these characters are just screwed no matter what, why should I care to keep watching? There has to be a balance to it and a lot of writers just can't pull it off.

As with so many things, there's a TV Tropes page for it: Too Bleak, Stopped Caring.