The only reason for your unit to turn off is if you are operating on internal battery power.
If the battery runs down then the unit will turn off. If Auto-Power-Off is enabled, then the CDR810 will turn off after the appropriate timeout (see the FAQ regarding Setup Menu Options).
Check the battery icon
Look at the icon in the lower-right of the display. If you see a battery icon, then the unit is running on the internal battery. It is not getting power from the power cord, and your unit may turn off unexpectedly.
Check the power cord
Make sure that the power cord is fully seated in the CDR810. Also make sure that the LED is illuminated on the cigarette plug. If the LED does not light up, then the plug is not getting power from the cigarette socket. Try removing and reinserting the cigarette plug.