I dont think he is an alcoholic.
If he is an alcoholic, then one of the signs is that once he starts drinking, he cannot stop until he gets well and truly hammered.
If he is an alcoholic, and alcohol effects his dick, then you would have had these limp experiences since you first started going out with him, not in the last couple of days.
Going limp happens to the best of us at least once at some point in our lives. Maybe it was the alcohol, coupled with him being stressed for some reason.
I bet that the first time it happened it scared the shit out of him. He is feeling insecure and less of a man, which is the reason why he feels he has to bang and hurt you when you have sex (i.e. to show you he is still a man and can fuck you senseless – gross I know). He is so scared of this happening again, that all the way thru sex he is waiting to see if it is going to happen to him again, and focuses so much on this (instead of focusing on you dear) that his fear becomes self fulfilling. This is a nasty turn of events, as the next time round its going to be even more of a problem for him.
The stupid thing he is doing is that he is blaming you. You have nothing to do with this, and his blaming you shows how insecure he is.
Two things you can do:
1. Speak to him when he is not drunk. Tell him that you think he is a hunk and beef up his very weak and fragile ego. Tell him that you want to have fun and go out and get him some viagra. Tell him that while you want to have fun, he has to be gentle with you as he is very strong and can easily hurt you, and that you dont enjoy sex that much when he hurts you. Let him have the viagra, and hopefully he will build his confidence again and get over his insecurities, and he will not be needing viagra again.
2. If you cannot get him to stop blaming you after 1 above, then really, he is not worth your while. He has no right to abuse you and take it out on you. You are not his punching bag and you never will be. Have enough respect for yourself to not let him punch on you. Get out of the way, leave him, for he needs someone professional to help him, cos he will destroy you.
Hopefully number 1 works – the best choice. But number 2 is a good choice as well if 1 does not.
Good Luck