Possibly worms. Get some wazine at the feed store and use it in the water. Since you can't catch her, this would be the best way to worm.
A few days after you worm her, if she still has it, then I would switch and put Sulmet in the waterer for no more than 5 days. I sorta' doubt it's coccidiosis since that is usually a problem for babies, not older chickens...but it's still possible.
The other thing is possibly botulism. Usually they get pretty sick acting with both coccidiosis and botulism.
Check for ANY possible moldy feed and remove it immediately if you find it.
Just my suggestions...