High rating pets (ones with high STR/INT/high skills and HP is a small factor too) have a high risk of jumping, what I've found out indefinitely is STR/INT are without a doubt the biggest factors and there appears to be a colleration with slots and Barding Difficulty. Also hidden skill advancements will jump a pet, like for example giving a pet Bladeweave he will automatically learn bushido/ninjitsu skill, now if you go and teach that pet Fient/F.Whirlwind (which will only cost a 100 points now) the system will take that in as a "600 spend" still instead of the 100 it actually cost because the Barding Difficulty will jump like if the pet has learned something big.
Release and re-taming is the safest course if you are scared of pets jumping, this will reduce the barding difficulty and in my eyes the pets overall "strength", whether you class this as an exploit or not what we know is that release/tame no longer reduces pet slots and the ingame mechanics drop the pets skills if released, this has been part of the game for as long as I can remember.
"Ultimate Training" on an extremely high rating pet (4+ or more) has to be done with this method or what are we left with? you'll have to settle with 2-3 max rating pets to train, so I don't know how people feel about the methods but all I know is the system still needs some serious work (just stop pets jumping, that's it!).
edit - seems HP matters just as much as STR/INT/skills, just wasted a white cu, I have another but with much lower HP oh well :/
Ah I just had a thought again and on all the cu's I tested I trained them immediately without stable so the no stable thing used to ensure Nightmare's don't jump seems to be the best trick!