The trash bear's requests do not refresh... UNLESS it is a seasonal request at the end of the season, in which case it will refresh. That means when he asks for fish or forage, not for cooked dishes, and 2 of 4 requests are fish or forage while 2 of 4 are cooked dishes, like the ginger ale in this case. So yeah, sadly no refreshing. Gotta get the ginger ale this time.