I missed this when it was first posted, but agree with the peanut gallery that this is most likely stifles. That “stepped into a hole” or “leg falling off” description is classic. If you stand behind him when he walks, does he also wing his hocks and/or rotate his hind feet when he steps? That’s more weak quadriceps, but it’s often all part of the same puzzle.
If you’re still looking at treatment options, ask your vet about IM injections of Estrone; oddly enough, it works by loosening the ligaments. Done in conjunction with (correct!) rehab work, the horse can then build the surrounding muscles to better support the proper range of motion.
In addition to a steady diet of hills/transitions/poles/backing, my sticky stifled friend finally showed tremendous improvement when I added lots of deliberate shoulder-in and classical dressage school walk to our regular arena work. Jec Ballou’s website has lots of good exercises too.