Sounds like he's not engaging his hindquarters correctly, whether due to poor movement/musculature or joint pain. He's not a youngster, if I remember correctly? If he were mine, I would try him on a joint supplement (4Cyte is very good, or Legend), and start concentrating on helping him work from his hind end in harness. Lots of correct bending to weight the inside hind leg, frequent transitions, and encouraging him to move with good impulsion. If you're unsure what you're looking for, Horse Gaits, Balance and Movement by Susan Harris is a great book with excellent descriptions and detailed diagrams to help recognise good vs bad movement, as well as information on the physical issues that result.
Further investigation with a veterinarian and chiropractor never hurts - except your bank account, but if they don't find anything wrong, at least you'll have purchased some peace of mind that he's not hurting. Good luck with him!