hens feathers breaking?

I don't think the feathers break off when they're going through a molt. My guess would be mites. Check under her wings and around her vent for little, brown creepy-crawlies running around. If you don't see any, wait until night time, take a flash light with you, pick her up and check again (some mites are nocturnal and can only be seen at night).
If you see them, treat with Sevin Dust (twice, 10 days apart), and use DE in and around your coop, dust bath areas, nesting boxes, and everywhere else your chooks hang out. You'll also have to clean out your coop and treat it against the mites (I had a pretty bad case last spring, but not again since then, because I whitewash the inside of my coop with a mix of DE and water, and use DE constantly).

Mites or lice.  The bugs bother the chickens so badly that the chickens break off or pull their feathers out trying to get relief of the biting and itching.  Treat immediately with poultry dust.  It will kill both bugs.  If you don't have that you can use Sevin. 

as granolamom stated treat again in 10 days and treat the entire coop.  Also give poultry vitamins that you can mix right in to water and up their protein.  The bugs can weaken them enough to get a secondary infection or disease and they can also kill the chickens if left untreated.

If you have a small number of chickens, there is a spray you can get at pet stores, designed for parrots.  Very easy to apply.  But as you have said, keeping the coop maintained is the ultimate answer.  You might also provide a sand box for your birds with sevin and food-grade diatomaceous earth in the sand.  Another substitute for Sevin is Dri-Kill which is a mix of sulfur and rotenone.

You can bathe them in dog flea/tick shampoo (or dip).  I have seen a "recipe" for making a dip with ivermectin, but don't recall the dilution.

Has anyone ever used or heard of anyone using Advantage, the flea medication, to treat mites? I am a veterinary technician and our Bayer Rep said you could use it. I feel like I have heard it from someone else too. One of my girls looks terrible, her feathers are breaking off at the base and in random areas. None of the other girls are showing any other signs. I am afraid to use Sevin as I am trying to be pesticide free so we can get bees, is Sevin safe? Help, I have juveniles in another coop and babies on the way.