At age 16, this relationship may seem important to hold on to mainly because you don't have much else to compare it to. I wouldn't say you should never love someone with emotional problems. But this poor girl sounds like quite a basket case. I'm sorry for her situation, especially her living with an abusive father. Unfortunately, you taking on the role of being her savior probably isn't going to work out too well. She seems to feel hopeless about herself, which is why she self-harms and is into substance abuse. I think you can support someone's efforts to help themself, but you can't do it for them. You're looking at a tragic situation that you would like to turn around. So you've tried your hardest, but you don't see that you're getting anywhere. That won't change anytime soon. Throwing your lot in with hers on a long-term basis will probably just mean that she'll somehow take you down with her. Self-destructiveness is like that.

All I can think of is that you might want to transition into being a friend, instead of a boyfriend. Right now, you may be letting her overly rely on you, so she gives no thought to what she needs to do for herself. Beware of emotional blackmail, whereby she threatens self-harm, if you aren't accommodating whatever she wants. Don't enable her resorting to manipulative behaviors.

I know the commonly accepted explanation for self-harming is that it relieves tension and stress. I've been around a few self-harmers, and I believe there is an element of manipulativeness in this behavior. The person feels powerless and without resources, so they are convinced they must be rescued. It can be a sincere belief, but it shifts their focus to wanting you to fix their situation, which you're not in a position to do.

Maybe there is a role for civil authorities to play, if she is being abused by her father. If the abuse is mainly verbal, they probably won't do much. Is this girl getting any professional help? Maybe you could offer to go with her to a school counselor to discuss what support might be available to her in the community. Someone - besides only you - needs to be offering this girl a hand-up. Try to help her find that. If she declines to pursue any such help, then you're fighting a losing battle. You won't help her, and you'll damage your own life. That's the sad reality.