Funny how he's embarrassed that someone should find out that he is doing whatever he can to save his own life and his marriage and ability to raise his child with you, but he's not embarrassed to live as an alcoholic, with all the shameful behavior that that can encompass? One of the defenses my AH uses is that he believes that everyone loves him as the party guy, even though he regularly crosses the line from party guy to passed out incoherent, slobbering guy--and people see that too. Not sure how lovable THAT is. My AH also won't do AA.
If you feel that you "know" it's time to leave, I would back up those who said that fear of bailing out on him is not a good reason to stay. You can't control what he'll do, whether you stay or you go.