I've read in one other topic where someone forfeited a match against a Valk for a friend and it despawned, so perhaps it does have a chance to change its spawn location.
In response to Ril, I have both but I prefer the B/B as I mainly got it for Beasts of Fable (although I hear they're pretty nice in PVP as well). I use a team mentioned somewhere on the forums, Valk/Water Spirit/Chrominius, and go Unholy Ascension/CoD->swap to Water->Geyser/Whirlpool->swap to Chrom->Howl (CoD/Geyser/Whirlpool land this turn, 1 shots every beast I've fought so far) if that doesn't do it, Surge of Power for cleanup. My point though, since I'm sacrificing it anyway I'd rather have the extra power, although either breed should suffice

.