Thanks, Jayne, for the links to the websites describing EPM. That was where I was going.
Your vet can do a series of tests for neurological function on the horse, to check if he is having issues. If the tests display a neurological malfunction (excuse my wording, I am not a vet), one of the causes could be lesions on the spinal chord caused by the protozoa responsible for Equine Protozoal Myeloencephalitis. These lesions occur when the protozoa, which are already present in many horses (thus the high incidence of them showing up in bloodwork, rendering the blood test insufficient), cross the blood-brain barrier and infect the spinal chord, which usually happens as a result of a lowered or depressed immune system due to stress, activity, or illness.
There are treatments available for it, one of which is the brand Marquis (Ponazuril), made by Bayer. My horse had three consecutive months of treatment, along with slow, steady work at the walk and trot, with uphill work to help rebuild his hindquarter muscles. He still has some difficulty with his left lead at the canter and will canter disunited on occasion, but overall his neurological function is good and he is safe to ride.
I'm not saying that this is what your horse has, but the symptoms are eerily familiar to me, and as EPM is degenerative and can cause permanent neurological damage, I would address the possibility with your vet sooner rather than later.
Good luck to you, and hope it's not EPM!
Tammy & Knight
The connection with the possums is that they are carriers of the protozoa, and exposure to their ***, either through grain contamination or through the water source, can increase the horse's chance of contracting fullblown EPM.