Haven't got one myself, but might be worth clicking on the Settings icon (normally a cog or two) and looking for "Daydream", possibly within a Display or Screen section.
If you've anything plugged into the USB sockets, try removing them temporarily and seeing if it still occurs. If you're connecting a USB hard drive that does NOT have its own power supply, and disconnecting this stops the issue, you could use a POWERED USB hub to sit inbetween the T95Z USB socket and your drive.
If that doesn't help/doesn't apply, try a factory reset (see
https://droidbox.co.uk/how-to/accessing-your-droidboxs-recovery-menu/ , you'll need to locate the switch on your model first). Once it has booted up, leave it alone a good 15 minutes. Then install NOTHING (for now). See if it still misbehaves. If it doesn't, install applications one or two at a time, and test for it turning off each time.
If still no joy, I'd email DroidBOX (see my sig for details).
Final thought, in terms of the box turning itself off, is it completely off, or sleeping? Can you wake it up using the infrared (simple) remote control?