Appeals Committee. Disputed situations in tournaments.

Sav, by the way, I've always wanted to know, isn't morality in Heroes purely mathematical? Sometimes it seems that way (and it's not just my impression) that creatures become demoralized simply because the player's decision coincided with some AI's ideas about the "best" solution in a given situation.

Morality is simply random with a certain probability each turn. No AI is used there.
However, it should be noted that these are pseudo-random numbers, but they try to reproduce randomness, and if this fails (for example, the generator loops), it is more likely a bug.

The argument about the non-stalemate situation is very interesting. Especially considering that, in practice, for it to become a non-stalemate, one side must simply immediately and voluntarily surrender. It seems logical, but something feels off.

To make the situation non-stalemate, you just need to continue the game. As the number of attempts increases, the probability that demoralization will occur twice in a row approaches one.
You can even calculate: the probability of demoralization is 1/6, the probability of 2 in a row in 2 given rounds is 1/36. In total, for 500 pairs of rounds (i.e., 1000 rounds), the probability that 2 demoralizations will not occur in a pair is ~0.00008%. This is negligible (the probability of a misclick is likely to be higher). And this does not take into account all cases of 2 demoralizations (it may be the last round in some pair and the first in the next), with a full account, the probability will be even less.

The same is true for 3 demoralizations in a row, and so on, only more rounds will be required.

So, the outcome of the battle is quite clear here. And voluntary surrender is only needed to reduce the time spent on running these 1000 rounds, with the outcome still being clear. Just like in the game, you surrender after losing an army and artifacts.