One who upholds or supports that which props; one who, or that which, stays, stops, or restrains; also, colloquially, a horse, man, etc., that has endurance, as in a race.
A horse which has the endurance to race well over long distances. Sometimes a person will comment that a horse can 'stay all day'. This means the horse in question is a good stayer and will continue to race at a said pace for however long is asked of them.