I'd question if he was even sober for that length of time (3 years) before you met. He seems like a binge drinker with a pattern. Probably an established one.
Regardless, he is very ill and now in treatment. He is doing what he needs to but there are never any guarantees.
I suppose in any relationship that is draining I'd ask myself 'what am I getting out of this?'. He has no money because when he does he spends it on booze. You want this treatment to work but again, it is up to him to maintain his recovery and until he does for a good length of time, stepping back for a bit would be the best thing for both of you.
It is hard because you love him but he has put you through so much in a fairly short amount of time. Imagine if you had a child with him. How would it affect your life then? I think you know in your gut what the right thing to do is but put yourself first whatever you decide.
I'd also ask myself what am I getting from this relationship and person? What is it that he is doing for you right now in the state he is in.
It isn't easy. I know firsthand but until he really takes recovery seriously and lives it, it will be like walking in a mine field of drama, tears and disappointment.