First of all, I want to say that you're completely justified in feeling burnt out and frustrated. It doesn't make you any less of a loving parent, and it is normal when dealing with anyone with a severe mental illness.
You did not fail her. You didn't cause this, and it sounds like you're doing everything you can to get her the help she needs. The only way you can fail her is if you deliberately sabotage her recovery or give up on her altogether. I can't imagine you are intending on either of these things. You WILL make mistakes along the way, and you'll have regrets on how you could've/ should've/ would've handled something. But therapy is the right way to handle those common errors and your mistakes only make you human, not a bad father.
As you're probably aware, personality disorders are vicious things. I have Borderline PD myself so I'm not just saying that to be mean. They're not easily cured, a person goes to therapy to learn healthy coping mechanisms and thought patterns rather than to get a quick miracle cure. Because of the pervasiveness (I hope that's the right word) and severity of personality disorders, recovery is NOT linear. There are backwards steps all the time. Add normal teenage hormones to that...she's having a rough time and of course so are the people who are affected by her behaviors. I'm not at all surprised that she's acting out, simply because of her age. It's hard as hell being a teenage girl with a miswired brain (that's how I describe my illness anyway, I realize that it isn't a politically correct or scientific description, but it's most definitely not meant as an insult).
Keep on with therapy. Individual for both of you as well as family therapy. Set boundaries - her actions should have consequences - but don't shame her or humiliate her. Be sympathetic as much as you can (you'll have to dig real deep at times). And encourage her every time she makes a step in her recovery. Every time she fights an unhealthy instinct, she has won a huge battle and that deserves recognition. Because a lot of personality disorder recovery is learning to act like a "normal" person, our actual effort goes unnoticed because the things we're fighting to learn are things that come effortlessly to most people.
Sorry I can't be more help, I more wanted to encourage you to keep doing your best with her. I wish my mom had recognized my disorder earlier, it may have saved me and others around me a lot of heartache, so it's nice to see a parent who puts in an effort.