That certainly hasn't been easy for you — let's see what's going on.
When did it start happening? Are you using the original power cable and adapter? Also, when it switch off are you still seeing lights on it?
Make sure your device is plug directly into a wall outlet. Your device should be within 15-20 feet of your router. Try resetting your Home Mini to its default settings.
Let us know how it goes.
I want to ensure you are good to go, and everything is working properly. Please let me know if you are still having trouble, as I will be locking the thread in 24 hours due to inactivity.