I do like the idea of having it so that species informs the decay rate of the loyalty. As I see it, the natural decay rates would follow something along these lines:
slowest: Unlife, non-intelligent Undead (zombies, for instance), Lawful non-humanoid creatures
very slow: Any animal that is routinely domesticated (such as dogs), Lawful human and humanoid creatures, and creatures considered "noble" (Dragons, Griffons, etc)
somewhat slow: Neutral humanoid creatures (eg/ Beggars) and creatures used to following orders (Giant ants/bees, for instance), Gargoyles and Margoyles
average: Anything not noted in other categories, especially animals that are known for being tamed, but not particularly loyal (Bears, felines, rats), Eyes
somewhat fast: Animals not known for being tamed (insects, reptiles, wolves, bats, Rabid Dogs), Chaotic humanoids who aren't either berserk types or criminal types
very fast: Intelligent undead (eg/ Liches), Wyrms, Quicklings, Pixies, Chaotic animal hybrids (Owlbears, for instance), Demons, Minotaurs, Mimics, Doppelgangers, Rust Monsters, Ghosts, Summoners, Elementals, Grues
fastest: Chaos creatures, Black unicorns, Gibbering Mouthers, Worms, Chaotic humanoid berserk types and criminals, Shadow creatures (note: not Shadows themselves, they're Intelligent Undead), and some special cases (for instance, Karmic Dragons)
Note that there would also be some special cases of un-tameable creatures, like the completely mindless blobs, slimes, and gelatinous cubes, as well as all unique NPCs unless specifically chosen to be tameable (as an example, there's Hawkslayer in ADoM, an unique NPC that can be tame).
EDIT: Perhaps there could also be effects of character and creature stats. For instance, I could definitely see a justification for difference in Willpower between PC and pet could influence either loyalty decay rate or chance of losing pet status given the loyalty level. I could also see pet's Learning influencing tameability, making the creature harder to tame but more loyal, perhaps?