If you fail the trivia and try leaving the area, coming back, and cutting the grass again, Keaton won't reappear. You'll need to use the Song of Time to reset events and you should get him to show up when you go back after doing so.
I'd suggest finishing up any other quests you have started progressing before you play the song, though.
I've only ever got the mountain village Keaton to appear once but failed the trivia so I went back to the first day, beat the boss and went back to mountain village but no luck. I've beaten the trivia and the other two Keaton locations.