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Mesprit does flee from the battles normally at the beginning. But if you manage to inflict damage on it then when you see it again it will still have the damage to it. The best way I found to catch Mesprit is to get a level 30-40 Pokemon that knows Mean Look, I evolved my gastly as i found my captured Haunters didnt know Mean Look. Then give your Pokemon that knows mean look a quick claw. Track down Mesprit using the Poketech app (forgot what it is called, my apologies >.
Use Electric Types To Paralyze The Get The Life Low And Use Ultra Or Great Ball.
Mesprit or Cressalia. They are both running Pokemon, so they are very hard to catch.
Its hard, but try catching it at night when dusk balls work. hope this helps
A Master Ball