There's a little Trick to save the Game when you want it.
Important: Items you have collected for the Riddles will not be saved (that's how I have experience it) and retour to the original Places.

To save the Game, just do this:

1. Go into the Lift who connect the Carter House with the Area below the Dam
2. Activate the Lift and wait until it has move a bit
3. Press Stop
4. Retour the Lift back to the Entrance, where you have start
5. When the Lift stop, the Game will be saved

The lift in the Mine will do it maybe too, but the Way is longer.
Other Places who save every time you use it will work too.