I want to know because they are impossible for me to catch. By the time I feel like I can catch them they use struggle and faint.
Yes, just defeat the Elite Four. They will reappear.
You have to defeat the elite four again.
Source: http://www.supercheats.com/nintendods/questions/pokemondiamond/188368/If-you-defeat-mesprit-azelf.htm and experience.
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