Hi JKS.
In healthy relationships, we come to love a person because of the potential we see in them as human beings. We then love them, and it is through our love that the other is able to approach, achieve and sometimes supercede what we perceived as their potential. In this way, our love for them grows. It's the same way with our own sense of self worth.
To the extent that the other person derails, postpones or destroys their potential, love wanes in healthy relationships. This is described in such thoughts as, "She's not the person I thought she was." This is not the same as accepting or not the person as he or she is. We can only truly come to know someone after having spent a great deal of time with them, through good times and bad. Depending on the outcome of these encounters, our love either grows or dissipates, again, in healthy relationships.
Only you know what and how much you're willing to tolerate, though not absolutely. You may find yourself checking out of the relationship as a means of getting on with your own life, and you may also find yourself staying until what may be the bitter end, even though this may not be something you'd even consider at this moment.
Addicts and alcoholics do benefit from love and support, but those things alone are rarely enough to help someone stay clean and sober. It's all up to him, regardless of how much he may think or say he loves. In the throes of addiction, there is nothing as important as continuing to drink or to use. And whatever comes in second place is very far behind.