Most Mobile Devices have different power profiles. When the device is running on battery it will conserve power, which means that the range of signal and WiFi coverage is generally less than when it is plugged into a wall socket (usually there is a middle profile for USB supplied power).
This is probably an indication that there is weak signal in your area, and the MiFi needs the additional power to boost the signal. You can log a coverage query with MTN here:
It may also be good to test the device itself and see if the SIM performs better in a different device. It may also be a problem with the device's battery or power management.