Are you opening up for him to move over into the new lead or holding your inside leg tight against him?
You can push that leg off of him and step deeper into that stirrup to encourage him to move over into the new lead. Also, what are your hips doing? I'm assuming you're riding a western horse, but with the well trained all around (I'm talking pleasure, horsemanship, trail, and WR) horses especially we do so much control with our hips, that if you're just sitting there and using your feet he may not know to swap over, or could be locked up and trapped without that extra help.
Also, he may be on his forehand and isn't sitting back on his hock like he should be and would need to be to get the change. I'd say to video yourself and see what you are doing and what he is doing beneath you. It's hard to tell what's going on without a video. I would recommend renting Charlie and Jason's video on teaching lead changes and seeing if that would help you.