After traveling long distances on a horse, the horse disappears immediately after dismounting. I haven't pinpointed an exact distance threshold, but it consistently happens after traveling roughly 1,000 blocks, give or take a few hundred.

The horse only reappears after re-logging in. It reappears in the same location where the dismount occurred.

The only seemingly relevant output in the log file is one instance of the following warning being thrown: "[Horse] moved wrongly."