He's not lame at all, and there are no health problems. His weight is good. He's just not a spring chicken, and he pushes hard and fast on the trail until he's tired.
So I think what I'm going to do is get off in the middle of the ride and make him take a snack break. Also, I'm going to switch him from Purina Senior to a hotter feed. I've got my eye on Omolene 500. My local feed store doesn't have a lot of options, but that looks like a good one.
I'll let you know how it goes.