I am so sorry about your poor cat!
Have you been to a veterinary neurologist?
What you are describing could be:
1. Feline Dysautonomia, which is a failure of the nervous system of unknown cause,
2. Or, it could be due to a lesion in the brain. Brain lesions can be caused by parasites, fungal infections, bacterial infections, tumors, trauma, stroke-like conditions, and metabolic disease.
3. Or, a lesion, very high up in the spinal cord, near the head, such as in the first few vertebrae.
Due to your cats age and the speed of progression the most likely cause may be a brain tumor. Brain tumors are not visible on X-Ray until the tumor actually damages the skull. Most of the time a CT scan or MRI is necessary to visualize a brain lesion. Analysis of cerebral spinal fluid may also be indicated.
Can you list which tests have been done? There can be so many different causes of neurological issues. Does your cat spend time outdoors? The first thing that pops into my mind is Baylis, a type of round worm common to raccoons and shed in their feces. Doesn't cause much trouble to the raccoon but often causes neurological problems in other species. I'm sure the doctor has a better list of suggestions.