I agree with keeping documentation about contacting parents, it will be beneficial to you. I would also talk to your school principal or counselor, I know that there may be times when a home visit has to be arranged in order to get parents to respond. My principal and counselor have gone on many visits not only to get in touch with a parent but also to "check out" what is going on in the home environment. There are many times where we as teachers also take on the role as parents, it sounds like this is one of those cases.

I would keep documentation of your efforts to contact parents, and schedule the student to be retained. When her parents inevitably learn of it, you will have to documentation to prove your attempts to contact them, and explain that it was your professional judgement that she be retained. I would also keep documentation of the student's lack of progress as evidence to support your suggestions.

In my school district, they usually send the parent coordinator out to visit the parents. Some parents simply do not have a ride. Although, I am unsure if that is the case here. My administration has also went to the lengths of suspending the students until a parent conference. If the parents dont want the students at home with them, that forces them to come in.