I'm guessing that stayer is not classified as common because most people on our side of the Pacific don't use that term much. Perhaps those who are into horse racing might know it, but most people here don't follow the horses much.
A great many of us Chi players have had similar moments of wondering why a particular word isn't common. A few weeks ago Tom wondered about the word rort, which is peculiar to Australia. I myself have wondered out loud in the Forum about the word plat, only to learn that outside of the United States, few people use this word, and not even that many inside the U.S. Many words have been reclassified as a result of discussions on the Forum, so people shouldn't hesitate to bring up any questions about common-ness.