I had the same problem, running Civ VI on Windows 10. For some reason no saves folder was created during installation, so I could not even save my configuration changes, let alone saving the game. Why the game gives no error when it is unable to save it,.. I don't know. @firaxis: this kind of issue is not acceptable when you release a game. If a save is not successful, the user should at least be notified.
Anyway, I was able to solve the problem by creating folders in the 'My Games' folder, i.e. C:\Users\(your account)\Documents\My Games\Sid Meier's Civilization VI\Saves
Step-by-step:
(edited the step 1 as I forgot to specify the folder - derp.)
Anyway, I was able to solve the problem by creating folders in the 'My Games' folder, i.e. C:\Users\(your account)\Documents\My Games\Sid Meier's Civilization VI\Saves
Step-by-step:
- Go to C:\Users\(your account)\Documents\My Games
- Add folder 'Sid Meier's Civilization VI' and open it
- Add folder 'Saves'
- Open Civ VI and save your game
- Check if it is actually saved in the folder; it should create a subfolder 'Single' and create the save game file in that folder
(edited the step 1 as I forgot to specify the folder - derp.)