I wouldn't put her down just yet. If you suspect a severe mite infestation I would give her a 'bath' in a flea/ mite solution.
Make up the solution in a tub with lukewarm water and then gently dip her whole body (not the head). As long as you have the solution made up dip the other chickens as well.
If it is mites you will have to clean all of the litter out of the coop, sweep very well and then make a white wash out of Sevin dust and water. Spray (someone mentioned using a pump sprayer for this and I think it is an ingenious idea) the walls, roost and nesting boxes. Make sure you get the cracks really well. Let it dry and then put fresh litter inside. It's a long process but if your chicken is that sick you don't want the others to get sick also.
The hen that is sick will need extra care. She needs to build herself back up. You can give her a few pieces of dry cat food (not dog food) everyday for a few weeks, scrambled egg, a few of her favorite treats and infant Poly Vi Sol vitamins WITHOUT IRON. These are baby liquid vitamins you can get at CVS. Give one drop in the morning and one drop at night for a week and then every other day for the next week.
If you have any questions just ask and I may have missed something so others will correct me. Don't give up on her.
