The first thing that comes to mind is worms. Have you ever dewormed her? If not, you can deworm the whole flock with a broad spectrum dewormer, I like Levamisole because it's easy to deworm the whole flock with it, but if you deworm them individually you can use Panacur (Safeguard), or Valbazen, (both good broad spectrum dewormers). don't delay, because worms can kill. Most vets will do a fecal float for you and then you will know for sure, and our vet does not mind giving us the dewormer (Panacur) for them too. Valbazen and Levamisole are available on line in various places. There is a withdrawal period after deworming before you can safely eat the eggs or meat; about three weeks, usually. Also, you should separate your sick hen from the others, in a place where she can have some warmth and privacy but still hear and see her friends. A rabbit cage or large dog crate works, if it's big enough she can turn around and walk around a bit. She could be losing feathers because she is molting, or because she is stressed from being ill, or both.