To open a point of discussion.
"Do horses go up in class until they rise above their class and never win anymore races?" Do they stop being contenders and become just racecard fillers?
They no longer are competitive in the new class and are penalised when they drop in class. How long do they langish in limbo until somebody realises that the horse is over-classed? At least in golf, if you have a blinder followed by your normal game, then your handicap starts going out again.