Uxie doesn't run away. Mesprit does. So don't worry.
In Pokémon Diamond and Pearl, you only have one chance to capture Uxie. If Uxie faints or if you run away, then you will not get another chance to capture it. The answer is no.
It will run away
in the middle of the lakes there are three caves azelf is in the one closest to your house mesprit is near pastiora city, but it runs away and you have to chase it and uxie is in the one near snowpoint city
it faints and disappears
it runs away
you get a 25 boost on stats .
he runs away
You cant find Uxie now because he turned into a Bidoof and ran away
it runs away?
i don't think anything happens.....
he runs away and you cant cach it
They will run away, and you have to find them in the wild and capture them.