I've noticed on occasion that some cavalry units will not chase routing troops. Double-right-click on a routing unit, and nada -- your unit might turn to face the routing troops, but that's it.

I've always found this frustrating, but it was especially so this evening as it cost me a battle. I was outnumbered 3-1 and my whole strategy relied on surprising (succeeded), routing (succeeded), and killing off the enemy's two best units (failed miserably because my general wouldn't run down the miserable buggers).

I don't think this is specific to EB. Any idea why some cavalry units occasionally do this?