Two different causes, I think. I imagine with the watchers it's just that they lose control when their leader routs. At least, I know I've seen a similar thing when leading mindless undead - the undead leader may panic and rout when he sees his army getting destroyed, which leaves them with no undead leadership, so they go leaderless and eventually collapse.
I think you'd have to set them to 99 (berserk) to assure that a unit never routs-except, guess what? I've had a berserk unit rout before! apparently-eventually-berserk wears off!
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You've sailed off the edge of the map--here there be badgers!