I think that sometimes, to inflict change in someone, something dramatic has to happen to kind of "wake" them up. And I say this based on what I've learned about myself when I was in a similar situation as your mate.
I think it's important that when your partner shows signs of self-hating, definitely let them know that they have someone who cares about them very much. Don't let them feel like they are alone. It seems like you've been doing a good job of this. However, there's a point where this becomes detrimental...
Maybe unconditional love and sympathy from you isn't going to help. It's almost encouraging that behavior in a sense. I think you need to maybe tell your partner that if they keep up this behavior, then you'll want to spend some time away from them until they get it figured out. It is a self-battle. And when you lose something that means a lot to you, it really makes you reflect on yourself. When you experience something painful (such as losing a relationship), it will break you mentally (at first), but then once you heal, you become stronger than you ever were. And that might be what your partner needs. Your partner has to WANT to get better, which is half the battle. Figuring out how to do it comes later. But something has to happen to get to that first step.