You can only save in the Sanctuaries between levels.

How?

I was in a sanctuary when I used the save from the Escape menu. Is there some other way?

I tried to save in the first sanctuary on the entry level. It would not let me. Do you need to get to the next level?

I don't remember the details, except you had to input a code, some runes, I think.

I always thought that you could only save in safe havens (sanctuaries, via backuo the game as an option) But playing the game right now I discovered that if you press esc you can save game in any place into the labyrinth.

Pressing S should save your position. No advice or message when you do it, though.
Later, starting the game should restore your party in your savegame position.

That doesn't work for me. I'm glad I figured this out before getting too deep in the dungeon.

Well, it works for me. Press ESC, a menu appears and the press S for Save. Q (Quit game) finishes your
playing session (automatically saving)

In fact the game autosaves during different critical moments like battles etc, overwriting the file and making the game similar to roguelikes. But additionally in Sanctuaries pressing ESC you can choose Save or Backup. This Backup option should function more like a traditional savegame creating a diffierent file than the former Save.

The save state file is called GAME.GMI and the Backup save file is called GAME.IMG both in the game folder.

One more note

Not sure if it can be the reason because I am playing with the default pregenerated party but if any of you have generated one party or more, this can be interesting, according to the manual:

"Multiple Parties with a Hard Disk
If playing from a hard disk, you can give a name to each party after
creating it, with a maximum of seven characters in the name. Then
you can select the party you wish to play with by typing UUKRUL
<partyname>, for example UUKRUL MYPARTY when you run the
game."

And according to Mobygames:

"There is a version of Uukrul that seemly does not recognize your newly created party...every time you save it or back it up, it fails to do so when you re-load or restore the back-up, reverting back to the default pre-generated party. To get rid of this annoying feature, follow the following steps:

[1] Create yourself a new party (if you haven't already done so) - and remember what name you saved the party under;
[2] Go to the folder where The Dark Heart of Uukrul is installed;
[3] Delete all files with the extension .GMI and .IMG, except 2 files using your party name;
[4] Rename your party files to GAME.GMI and GAME.IMG;
[5] Play game.

You will notice that can now load the game using your party."

Thanks! It's working now.
EDIT: Nevermind. Even when I delete the IMGs and GMI's it still remains the pre-generated party. I'm going to keep messing around with it.

Have you tried running your game with the party name command line? By default the GOG version runs "Uukrul -V" this is, in VGA Mode. Try running "Uukrul <Your party name> -V" to see if it works.

You can do it easily editing the file "dosboxUukrul_single.conf" for testing

Is this confirmed to be working?
Planning to pick up and dive into TDHoU by the end of the week and the last thing I need is the late realization that my custom party has been overwritten by the default one.

It's not working for me. But I'm sure I haven't tried everything. I haven't tried the above either. I've been busy. Decided to play with the pre-gen characters instead.

Having the same problem.

Esc ->S. Restart game. Nothing is saved. Whether itts in the sanctuary or not.

Would love to play this classic game, just not all in one sitting. :P

I installed it today via GOG Galaxy. Create a team of characters, allow it to overwrite default GAME (by pressing enter instead of typing party name). The save apparently works?

Just remember about the autosave and backups that has been mentioned above.

If you still facing issues, try uninstall and installed it inside different location (maybe folder write issues?).