3rd Gen hold up!!!

[Spyke]

1nce u find latias in sapphire and it runs can u find it again

 

[invinible]

That is when you can use the Pokedex to find it.

 

[Porygon]

Also, it remains at the health level [and condition] you left it at last time.

 

[Sleek]

and if you kill it, it doesnt come back...

 

[Manta~]

^-^

Yeah, You Can Find It. But Only If You DIDN'T Knock It Out.

Do You Have Gold Silver Or Crystal? Its Just Like The Legendary Dogs From That

 

[Arore]

Basically, it is just like the Legendary dogs: they can run, but their health doesn't go down, and you can track them once you find them, but it is difficult because they keep on running.

 

[DragonTrainer]

To summarize it up:

If you find latias/latios, you will find them at the same condidtion you left them off.You can track them with your pokedex after you encounter them once.Basically the same as legenday beasts/dogs.