I was still jumping my dad's 35 year old gelding when we had to put him down due to colic. We definitely had to limit how high they were, and he wasn't the best jumper lol, but he did have a lot of fun. But I also had a 19 year old gelding that was my jumping horse, was doing up to 2'6" with him, but shortly after he turned 19, he started refusing fences, which he'd never done before. After he started refusing even the low ones, we got the hint, and sold him to a nice trail home. Obviously the jumping was getting painful for him, or he just plain got tired of it, and needed a change of scenery. I would have kept him, but I still wanted to jump. Just make sure you are paying attention to what your horse is telling you, but there is no reason why he can't jump.