What you said
I would ignore the request and let it slide. If she asks you directly why you haven't accepted, a simple `I keep Facebook for friends I've known for a very long time outside school, but of course I'll continue to help you in school' should be enough.
Tell her: "There are rules saying I'm not allowed to do those things and I'd get in trouble."
The expert view
This is an issue many teachers face. It's great that you have made progress with this girl - that is a valuable relationship that could be vital in her education. But there need to be boundaries, and if she is fragile she might also be needy and liable to imagine that her teachers are her friends, which won't do. The teacher's role is one of authority, and the more she sees you as a pal, the more she will demand and expect from you. That could be awkward when she realises that you can't be a shoulder to cry on or a chum to cover for her.
Treat her with dignity by saying, as suggested above, that you can't add her as a friend because it's not allowed. If she says, "No one will know," you say, "I will." If she forces the issue, you will need to be more direct and say: "I don't add students and I don't want to." Don't let her think that you'd love to, only the nasty system prevents it.
I wouldn't bring it up unless she does - that way, she will get the message tacitly. Eventually, she will learn that you have boundaries that won't be crossed. Thus, she gets an adult that she can trust, and you get a clearer, less anxious relationship with a pupil.
Also, inform your line manager about the conversations so that you are covered if she takes it the wrong way.
Tom Bennett is author of The Behaviour Guru and Not Quite a Teacher. His latest book, Teacher, is published by Continuum. Post your questions at www.tes.co.ukbehaviour.