How's his canter?
Any problems with riding over the last year or so? Stiffness to one side, not extending, bucking?
I looked back at his April 2012 video with him galloping around the outdoor arena and he looks strange there too. Like he is running with both hind legs together. He is cross cantering a bit too.
I have a mare who cannot canter- I don't have a diagnosis. She knows where her feet are (can trot raised poles just fine). She falls to pieces at the canter. Bucking, cross cantering. Just uncomfortable. If you try cantering over poles she smashes them. Her joints look great on X rays. The vet thinks it is her pelvis (or maybe her spine?). She is not lame at the trot. She has muscle wasting over her back in the loin area only.
If you can afford it, get a nuclear scan. It is over $1000 depending on how much of the horse you want to do. Should light up if you have any problems in the bones (and should show if the spine is the problem). That is what my vet recommends next. Probably won't show lesions on the spinal cord- you need an MRI for that. A few places have horse sized MRI's...
This could be neuromuscular instead of neurological... I have a problem with my legs collapsing on me randomly- both legs are affected but usually only one leg collapses at a time. All testing has been normal, no nerve damage has been detected... The doctors are stumped. Could be a muscle problem...
Nerve damage is usually consistent or gradually gets either better or worse. If he dramatically changes from day to day, my guess would be it is a muscle problem or something else.
Can you retire him?