I've hung onto a bad marriage with an alcoholic/addict husband who has done the things that you have described. Always followed up by a truly lame "I'm sorry, it'll never happen again." And it has happened again. I did it for a long time on the basis of hope for the relationship that I think it can be. Not the relationship that it is. Hope is a powerful thing. It can carry us forward to do great things. It can also keep us stuck on stupid.
Since you aren't married to this guy. And you don't have children with this guy. And you aren't financially dependent on this guy, take him at face value. That this is the best that you can ever hope to achieve in this relationship. Is this how you want to live the rest of your life? I didn't think so. Focus on your own sobriety.