Azelf will disappear from the game once you flee from it in Pokémon Diamond. It cannot respawn in Pokémon Diamond since that feature for Legendary Pokémon was not implemented at that point in time.
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it is very hard to get azelf and mesprit and uxie. in my Pokemon diamond, azelf and mesprit fled the battle. if you want to find them, use your matching Pokemon app on your watch and DO NOT FLY UNDER ANY CONDITIONS. IF YOU FLY, THE POKEMON WILL ALSO FLY AND YOU WILL NEVER FIND THEM. DO NOT LOSE HOPE!!
Yes, Azelf will respawn, if you have fled or accidentally faint it, after defeating the Pokemon League.
Its not Azelf its Mesprit that flees and you get it by using the Pokemon tracker app and you wil need a Pokemon with mean look so Mesprit does not flee.
When you catch dialga/palkia or defeat them, you can catch azelf and uxie in the lakes.Mespirit will flee so you gotta get a poketech radar to track it down.
The bait in the great marsh makes a Pokemon stay longer. However if you use too much it could startle the Pokemon and make it flee. The mud when used makes a Pokemon easy to capture but has a high chance of making the Pokemon flee.