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

Battle save definitely adds time. Saving during a crash or manually saving doesn't. HD 4.208 RC5, HWrules 1.38. There's also a save at the beginning of the turn (I can't find the setting to enable it) – it gives you a free 10 minutes (the counter shows +9:59), separate from the main timer, which isn't affected. How to use this – who knows.