Hi 2020. There is a book that is often recommended here, Codependent no More by Melody Beattie, you might find that an interesting read.
I'm sure you are probably going through some hurt and pain at the moment and I'm sorry you are.
Unfortunately, alcoholics do not make great partners.
You ignoring him might have him drinking more, because that is how he copes with life. While if you were distraught you might call your friend or post here or go to the library to seek information, he just has a drink to temporarily shift his mood and outlook. It's his coping mechanism and that isn't changing, at least not right now, as he has stated.
I think it's really important to believe him. When he says he is not giving up drinking or getting help with it, he's telling you the truth. Now whether he does choose to get help 5-10 years down the road or never, again, has nothing to do with you.
You didn't Cause it, can't Control it and can't Cure it (the 3 c's).
He keeps texting that he loves you, however is that enough for you? Although you may both love each other, is that a good enough reason for allowing him to come back? I'm sure that's a question you are asking yourself.
Nothing has changed, he is the same person you asked to leave a week ago. Whether you want to continue on the ride is, of course, up to you, however don't expect it to change.
Originally Posted by
2020vision 
He usually reaches out after awhile and acknowledges his problem and doesn’t blame me for leaving him. I, being codependent, feel horrible and take him back. Who else is going to take care of him?
He will take care of himself and it might be the best thing for him.