Dana...I'm no expert on the sex-starved marriage (although sure not having any myself lately!) but your story triggered the memory of something I recently listened to in the Light His Fire audiobook. Is it always you trying to help him fix his problem why he's just given up and kinda depressed about it? Are the cheerleader that tells him it will get fixed eventually? There was a lady whose husband had other medical problems and depression...he was doing nothing about it and driving her crazy. I think the advice suggested was the next time he started moaning about how hopeless it all was...the therapist told her to tell him, "You know honey, I think you're right. I thought you could beat this and have been encouraging you all this time but now I see it's really hopeless. Maybe this problem really is something you can't do anything about." In this case her saying the opposite of what she normally said seemed to snap him to his senses and he started making some small steps to help himself and do positive things about the situation.
I don't know that this applies to your situation but to me this seems to be an example of Divorce Busting's "Trying a 180".