I agree with the others, maybe this is wishful thinking on your part? That is completely normal, but probably not good for you.
He hasn't given any indication he wants to quit and after you have broached the subject a few times, he has backed off, I think that is your answer.
Generally, with addiction, there are underlying reasons why he drinks, as you mentioned in his case, possibly as a coping mechanism. Pretty much everyone on earth knows that drinking copious amounts of alcohol is not good for you, but that is absolutely his choice.
Why does he keep in touch? He may think that a relationship with you would be nice, but he is, perhaps, realistic enough to know that isn't going to happen, that you are not willing to enter a relationship with an alcoholic. That is a good thing on his part (and yours). He has decided that, at least for now, he will drink.
Personally? You know what you know, you know this is going nowhere fast, is it possible if you continue this periodic contact that you are going to get hurt here?