Feeling alone

Things with my partner are not going well. I think it would be in my best interest to break up with him. He is an alcoholic and has been in rehab three times in the last nine months. Each time it takes more out of me as I take care of him while he's drinking and deal with the emotional and financial ramifications of him being gone for prolonged periods of time. Now he's home and he's been sober about a month and half but he is not doing well. I haven't been doing well. He has serious intimacy issues and he doesn't even touch me or really even talk to me. It makes me feel so alone. I've tried to talk to him about this a hundred times and each time he promises me he will try harder but never does. Now I've reached a point where I am coming to terms with the fact that the things I want and need in a relationship are different than his needs and what he is capable of giving in a relationship. But now that I've reached a point where I want to break up with him I feel like I can't because he is horribly depressed. He sleeps all day and doesn't eat. He doesn't talk. He just lays on the floor under a blanket. How can I break up with someone who is in such a terrible place? But what do I do when I am also depressed and in a very unhappy place in the relationship? I am tired of feeling alone and being a caretaker. I don't know what to do and I feel like a horrible person.