It should come back after you beat the Pokemon league or if you saved b4 battling Cobalion which most people do you can just turn off the ds/ds lite/dsi/dsi Xl and battle him
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No once any Pokemon has fainted you can not capture it sorry
Yes you can! After he faints go back and he'll be there.
You have two chances to catch Mesprit. If you accidentally make it faint both times, you can't catch it anymore. If you made Mesprit faint once, find it, trap it, lower its hp to 1 using false swipe (you should have gotten the TM), let it escape, then encounter it again and use a quick ball.
yes it will come back if you defeat the E4 and Lance. It will keep being that until you catch them. Same rules apply to other legendarys
you cant groudon (like other legendayrs) are a one time capture Pokemon, you get one shot and that's it you should save your game just before you fight them to insure this doesn't happen