My girlfriend has been having a somewhat similar issue. Her computer doesn't shut down entirely, but the screen goes completely black and she is unable to do anything but a hard shutdown even though the game sounds are still playing. My guess was that the game is overheating her graphics card so that it stops working, but the weird thing is that it seems to affect specific save files permanently once it happens. She can start a new world and play fine for a while, but once this happens in a save for the first time, it will then happen again as soon as she enters that world, every time, which doesn't seem to fit with overheating.
Best of luck solving this, GoblinGirl. Hope you're able to enjoy this game with your partner.