I wouldn't say that leaving one's partner for another woman is a "norm" for recovering alcoholics. I would say, though, that in early recovery--when the alcohol is gone but you still don't have your marbles back and your emotions are all over the place with no way to process them, it is very tough on relationships in general. Some make it and some don't.
Relationships are hard work, and usually by the time an alcoholic is finally ready to quit drinking, there has been a lot of damage done. Some find it too difficult to cope with, and sort of take the easy way out. I don't think it's possible to generalize--there are plenty of alcoholics who DO do the hard work. And there are some, probably, who stayed in relationships while drinking that they would have ended anyway if they were sober and able to cope on their own.