If it's a fundamental body issue (muscle soreness, in need of an adjustment, a health problem like arthritis or lameness, etc) I wouldn't expect the horse to be able to pick up the lead in a round pen all of the time. If the horse picks it up in the round pen just fine every time, but can't under saddle... this says that the problem relates to the rider or the action of riding. For example, poor saddle fit, horse is imbalanced by the weight of a rider (either because they lack the muscle to balance with a rider on board or the rider is throwing the horse off balance), a health problem is exacerbated by the weight of a rider, and things like that.
In most of these situations, the problem relates to stiffness (inability to stretch on one side) anyway! For example, my gelding couldn't pick up the left lead under saddle but picked it up on his own in the round pen just fine. Turned out that he was inadequately muscled/balanced so that with a rider, he just couldn't do it as easily. My solution was to really really collect him up right before the transition, and if I collected him properly, he'd pick up the lead without issue. I also found that he was stiff going to the left, so we did a lot of bending and lateral work, and I'd make sure that he was well-warmed up before cantering. After a while working in that way, he built the muscle and balance to pick up the left lead without the conscientious effort of super-collecting him every single time. But, we still work on stretching out that stiff side!
Last edited by existentialpony; 06-19-2013 at 11:28 PM.