How many times do you have to defeat Rayquaza to get him to join on explorers of sky?

In "Pokémon Mystery Dungeon: Explorers of Sky," you need to defeat Rayquaza once in the main storyline to unlock the opportunity to recruit him. After defeating him, players can then attempt to recruit Rayquaza by returning to the Sky Pillar. The recruitment chance can be influenced by the player's overall team level and other factors, but defeating him again is not necessary for recruitment.