The Collaborative International Dictionary of English v.0.48:

Stayer \Stay"er\ (st[=a]"[~e]r), n.
   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.
   [1913 Webster]

WordNet (r) 3.0 (2006):

stayer
    n 1: a person or other animal having powers of endurance or
         perseverance; "the horse that won the race is a good
         stayer"