That's true for any weapon. Shields break, weapons don't.
I have more issues with the fact that it is so easy to run the AI on horse, into a wall. Then he'll just stand there for a while and you ram a lance into his back. Really easy. Just run around in circles a bit and he'll hit a wall eventually.
Horsed AI sucks in tournaments (probably in battles too, but you don't notice it as much).