Rep whores can change their own whenever they please, but I don't know how it works for the winners (or in some cases, losers) of previous contests. I'm pretty sure they are stuck with the ones they ended up with.

If there was an option, I suppose it would have to be change as often as you want, so it would work the same way an enlarged avatar or signature would.

That presumes of course, that the mods are not doing special things to get around the normal size boundaries. In either case, I would think that it should be the same for all three prizes, whichever way it works.