J.M.
I would actually do the opposite of what you are doing. The problem isn't entirely that other kids are mean to her (although they are starting to be), the problem is that she is irrationally sensitive. At least that's how I'm reading it.
I would encourage her to not indulge in those feelings. My daughter is also very sensitive, and she will often say "So and so said such and such and it hurt my feelings." I will often counter by saying that what her friend said wasn't mean, and that if her feelings were hurt, that was her choice. I think that it's important that she learn that the world is not out to wound her, and that it really is a choice to feel bad about everything. Right now her irrational thought pattern is being fed as well because her unhappiness is getting your attention. Obviously she's not doing it intentionally, but that positive attention is really gratifying. I think that if she gets less attention for her maladaptive behavior, and more attention for good behavior, it might help cut it down.
I also think that it wouldn't hurt to get her hooked in with a child therapist. I don't think that she needs a diagnosis, but I do know that people can get into negative thought patterns which can later lead to depression. Better to break the habit now.
Good luck.