HoMM3 HD is a mod (add-on) for the game Heroes of Might and Magic 3.

rebellious, this is truly a "native" bug of "Heroes," because I checked: it appears in both the "pure" SoD and the "pure" Complete Collection (NOT under the HD mod).

the save doesn't load for some reason in multiplayer mode

And it shouldn't, I think: the map is a single-player one!

and your hero defeats the enemy, with losses, of course.

The point is that I don't need such a Pyrrhic victory: I don't need to hold this city (even if it's an allied city, not mine!) at any cost, but the troops are invaluable! I'll get stronger, and then I'll defeat the necromancers. I've already defeated the main barbarian hero, and soon the barbarians will be defeated; then I'll deal with the necromancers. I'll tell you how it goes. The map is called Undead Apocalypse, from the maps4heroes website.