I don't know if there's a set date for this mini game, but when I encountered it in game, there was an error *right when I crossed the finish line* So I had to rollback and retry, but it still showed me error messages so I ultimately had to decline the challenge. And this happened right before July. Also, I think there's a mistake in the game's calendar. July 1st occurred twice for me (Sat and Sun) so I had to pay wages and fees twice.