((((( wisewoman )))))
I am just finishing up a book called, Another Place At The Table by Kathy Harrison. It is mainly written from the perspective of foster parents but it also gave me an insight as to how these children have such deep rooted issues of being "abandoned" by their birth parents and how it interferes with their lives, even if they are placed in a loving family such as yours.
Not everything is your fault.

You gave her a roof, food, and loving arms. It's up to her now to find her way.
Battered women go back to their abusers. I suspect that's what's going on here.
I hope the loving arms you offered will lead her back to you someday.
Peace,
Petunia