J.B.
Therapy, yesterday. We're in a very similar situation with my 14-year-old SD. Her mom sent her to live with us "temporarily" last year while she looked for an apartment near us and then moved to another state, then moved again to a different state to live with a guy. She's only an hour away but doesn't call, text, or visit. The only time SD has seen her mother in 14 months was when she came for 2 hours on her birthday, which her mom made a big deal about and then disappeared again.
It took lots of time and many therapists to find one that SD would talk to, but it has made a big difference. This isn't for your SD to feel like she's a freak or that something is wrong with her, but for her to understand that she had undergone a trauma (abandonment and separation, repeatedly) and needs to process that trauma in a safe place so that she can heal and live a full life where she experiences a full range of emotions in a healthy way and will be able to have healthy relationships with all of the important people in her life. Once my SD started talking, it really only took a few months of weekly sessions for her therapist (who is also working with our other kids) to say that he only needs to check in with her once a month or whenever she feels like talking to him.
My SD still has a tendency to isolate herself in our home. She does a lot of solitary activities like drawing, painting, web design and listening to music and is surrounded by three brothers and doesn't participate in their recreation (hockey, video games) so we really have to make a conscious effort to include her in things and draw her out. I have to deliberately invite her into the kitchen to help with dinner, or suggest that she bring her laptop into the family room so that she can be on-line but with us. It's tough at this age because the solitary thing is a normal and age-appropriate phase, but for kids who are dealing with abandonment, it's important to be deliberate about connections. Our family therapist has been helpful with suggesting ways to stay connected that aren't intrusive and don't make her feel like we're violating her privacy (like offer to be the one who drives her and a friend to the movies, invite her to join me when I go to the gym, my husband takes her to boxing and kickboxing and watches her classes etc.).