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

3.04 – the same bug is present again. I can provide a save file if needed.

In 3.03, I verified – it was indeed happening! I found the cause (I simply forgot to include parentheses in the expression, which caused the following to occur before replaying:
instead of 18 + (GameType >= SoD) artifacts for the doll, 18 + GameType >= SoD were restored,
meaning that instead of 18 for RoE/AB or 19 for SoD, 1 artifact for the doll was restored.
I fixed it. I definitely fixed it! I tested the fix and confirmed it worked several times. The fix was definitely uploaded to the website and the download page. After the last report, I downloaded and tested it again. Everything is okay.
So, please provide the save file. Also, please provide the HD_CRASH_INFO.TXT file generated by pressing [CTRL]+[ALT]+[SHIFT]+[DEL] in the game. Although, you can just tell me the version number of HD indicated in the beginning of the file, instead of sending the text file.