I read this earlier and I've thought of it off and on all afternoon.
You don't say how old the two of you are. That may make a difference in a situation like this, as to whether one or both of you are going to be out of the parental house any time soon.
As the situation stands, though, it sounds like the best option for all involved may be to respect the wishes of her parents--not because they're right, but because it sounds like your girlfriend's life is being made pretty miserable.
If she has been having issues with not being able to see you enough in the past, and now you can't see or talk to her at all, it sounds like this relationship will not be able to work for her. It doesn't sound like a particularly pleasant spot for you, either.
I don't think hiding it is the answer; that may just bring about more extreme reaction from her parents when they find out (and they will--parents, somehow, always know). It sounds to me like this may spell the end of your relationship, and while that's sad, it may be the best thing for all involved until she is able to free herself from the restrictions of her parents.
"And when the answer that you want/Is in the question that you state/Come what may..." - Coheed and Cambria, "Blood Red Summer"