Inexpensive battery pack doesn't have a low voltage cut off
Use a micro controller to monitor battery voltage and toggle an N-Channel Mosfet on/off.
Works like a champ! As you can see in the picture the green test LED shuts off 9.3VDC and comes back on at 9.32VDC.
My particular battery pack has three 3.7 volt cells. with a recommended discharge voltage of 3.1V per cell. So 3X3.1=9.3VDC.
The circuit does have a 100K trim pot. So it can be set to any voltage that is needed. to calibrate just set a power supply to the desired voltage and adjust the trim pot until the led turns off.
This set up uses an IRF510 but could be swapped out with something smaller or larger depending on current requirements.