When playing singleplayer Hellfire, the game crashes when I try to save, forgets what I was doing, and forces me to start a new game. I've never yet made it past level 2 of the Cathedral, because it also sometimes happens when I die. I sent GoG an email requesting help, and got a robot response saying it would be weeks. I've tried numerous workarounds, and haven't been able to fix it. What can I do? I want to play the game, and it's impossible to progress like this; plus I paid money for the stupid thing. I've never had a GoG game fail on me like this before. Windows 8, if that helps. Thanks in advance

it needs permission to write to disk. from your OS or antivirus.

add the game folder to exceptions. it should help.
test by starting a new character and immediately saving.

It's already whitelisted in my antivirus, and I have it set to run as administrator. Still not working

Maybe that's not what you meant, though. The exact error message is "Unable to write save file archive." How do I give it the permission it needs?

I Googled how to give a program permission, and found this...as you can see, my settings already match the recommendation. Diablo isn't even installed in Program Files or (x86). I've also tried reinstalling it once already.

One of the crashes just deleted my character. The save file is still in the folder, but the game is only offering me to start a new character.

Following. I'm having this exact issue as well.

same as well for me on both diablo and hellfire

I would suggest you try using DevilutionX to play the game, it fixes many of the bugs in Hellfire and is compatible with modern operating systems so that you do not need workarounds or admin privileges:
https://github.com/diasurgical/devilutionX/releases

I am having a bug that occurs when I go to another area (i.e. town portal, deeper in the cathedral) soon after gaining a level (in single player). This was with DevilutionX and playing Hellfire. I will be testing to see if doing 'New Game' right after a level maintains the character.

Well thanks for DESCRIBING the bug ...