Question

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.

Answer 1

Yes, just defeat the Elite Four. They will reappear.

Comments

What happens if they start using stuggle again and faint? Do they come back?

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Beat the elite four again.

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So I just have to keep beating the elite four to get them back. Thanks!

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no problem.

Answer 2

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.