Length of henopause varies by breed. But if she’s 6, hopefully this will be her last year laying. My 6 1/2 year old light Brahama stopped laying last year as did my 6 1/2 year old buff Cochin. My white Cochin sadly died last spring at age 5 1/2, from vent prolapse after I couldn’t remove her 3rd bound egg.
Are you giving her vitamins and mineral supplements like previously discussed? Losing balance from perch could be vitamin B-12 deficiency which causes neurological issues including loss of balance. Older hens need extra vitamins just like older people. Please make sure she’s hydrated and getting enough vitamin B-12, D, E and calcium. With B-12 and E being most important to stave off neurological disorders.