It could be a health issue, but I wouldn't be as too sure from what, but I have observed that a lot of horses have a preferred lead. They may spend all their time going on that one lead their entire lives, building up muscles to only support that lead at the canter. So when a person tries to get them to pick up the opposite lead, they find it hard and the person on their back adds to the struggle. Why do it the hard way when it makes you tired, when you could do it the easy way?
I would have worked on lunging on the bad side, making a small circle so even the easy way would be hard, trying a lot of trot-canter transitions, giving a lot of praise when the correct is picked up and let the horse move on a big circle. While making a small circle if it is incorrect while shaking the lunge line until a trot is achieved and then ask again.
When the horse can efficiently canter on the lunge, I would do the same undersaddle. Trot on a small circle in the direction of the bad lead, ask for canter, if the correct lead is picked up, encourage the horse to go for a few strides while verbal praising, then slow to trot and praise again. If the wrong is picked up, do a small circle on the incorrect lead to let the horse struggle, then ask for the trot and ask again.
Eventually you hope to build the muscles needed to maintain that lead. Its like working out one arm and expecting the other to get in shape too. Its different muscles.