You cannot re-battle Azelf once beating it if it's in Pokémon Diamond or Pokémon Pearl however if you knock it out in Pokémon Platinum, Pokémon Black 2 or Pokémon White 2 then you will be able to re-battle it. As of Pokémon Platinum, there was a new re-spawning feature that was implemented for Legendary Pokémon that will allow you to re-spawn them if you have knocked them out, all you have to do is head to the Pokémon League and beat the Champion.
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If you knock out Azelf in Pokemon Diamond, Azelf will be gone forever (unless you have saved before battling Azelf and shut off the game and turn it back on to try again).
You cannot rebattle Gym Leader in Pokemon White.
You cannot rebattle legendary pokemon. (Correction, Giratina is on Platinum ONLY)
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Rebattle Shaymin 94000130 fcff0000 B21c4d28 00000000 B0000004 00000000 20001295 00000000 D2000000 00000000