Perhaps they become extinguished? I'm saying this because that's what happened in the cartoon episode "Reign Storm". In the episode (available on DVD), Ludwig builds a (rather unconvincing) robot duplicate of Peach and has her/it cause problems for Grassland. Among RoboPeach's orders are extinguishing all the Fire Flowers, and we see some firemen watering the Fire Flowers while hearing the "Power Down" SFX.