My doctor put me on a birth control pill called Lybrel that stops your cycle as well. It caused depression in me, so I had to come off it. But I don't think hair loss is a side-effect of it.

From what I understand, it can also be a side effect of some illnesses. I think it can happen with hypo- or hyper- thyroid, for example.

If it were me, I would probably talk to my doctor about it.