Pictures of your hen might be helpful. Does she still lay/has she been laying? Any other symptoms like pale comb, respiratory issues, or water belly? Have you checked your birds and the coop for mites/lice? When was the last time they were dewormed?
The balance and head issues may simply be from lack of nutrition since she isn't eating enough. I'd put some poultry vitamins in her water or food and encourage her to eat with some tasty treats like scrambled egg or tuna and see if she improves with a little TLC. At 4 yrs old she could have cancer or some other fatal disease causing her general decline, but it's always good to look for treatable issues.