The game is not saved by setting the options to Stop Time. That setting pauses the game, but the only way to preserve that setting is to either click Play or to return to the menu and click on Exit. The game is automatically saved every 30 minutes, as well as each time you exit the game.

If you leave the game on the options screen with Stop Time selected and subsequently change the speed to another setting and click Play, the game will update everything at the new setting, in essence ignoring the fact that it had been set to Stop Time. That's an unfortuante side-effect of the way that the options were implemented. The only safe thing to do after changing the game speed is to either click Play or Exit, which will save the game with those new settings.