PET XP STOP: I've had this as well. I suspect it happens when you become reborn. Perhaps your pet can't be more than a few levels above CURRENT level? Maybe lower regions only provide xp up to a point? Or maybe its just a rebirth bug.
Reebo is correct, you can get a pet when only the highest tiers of loot are checked off. Thesis rejected. However I am still curious about the Max of LVL 34 (with 51k xp) on the pets.
PETS: I didn't get any until I checked all loot boxes. Both pets I've received are GREY quality. It may be that you won't get most pets if you eliminate the lower loot tiers? Also: My first pet was okay since it gained a defense ability (for a total of three abilities, two from start)... However it has topped off at Level 34 (with 51k xp), and won't gain anymore. My second one has no abilities. It usually dies on one hit, and does only 1 damage. Pretty much only useful to take away one hit from the tougher opponents.