I've noticed that the assistant doesn't scold you when you shut off the game without ending first. However, due to the lack of a numerical loyalty index, I can't tell for sure if my monster suffered some sort of penalty.

Would you mind listing the loyalty levels you've seen thus far, Thorr?

I have seen only 3 (but I think there are 4 total)

SInce it's character based, it's hard to give a good translation, but I have seen -
1) Colleagues (Starting value)
2) Mutual Respect (No translation site gives me a good version of this, so this is my best guess)
3) not recorded..
4) Best Friends (Most trusted person)

I believe these are quantified every 25 points, just like the Popularity -

1) Nobody
2) not recorded
3) Star
4) Hero

Well, that makes sense.

Which one has the horizontal line as the first character? That's what my current monster's loyalty is. My brand new Pixie, Mimi, has two kanji characters, so I think it's safe to assume that my other monster is more loyal.

I'm going to start screwing around with what affects loyalty. First off, I'm going to repeatedly freeze and unfreeze my more experienced monster to see if its loyalty drops any.

The horizontal line is the Kanji for "ichi" meaning 1. It the highest loyalty.

Nice! Now to for a little disenchantment.

Well, I failed. After freezing and unfreezing over 30 times, my monster and I are still inseparable. Its loyalty level hasn't budged, and it never fools around in battle. I think it's safe to say that freezing has no significant effect on loyalty.