Somewhere in your inverter, there should be a potmeter (or a few resistors) that set the threshold at which the inverter should switch off due to low voltage.
This potmeter may be clearly marked on the board. If it's instead a few resistors, you could play with the values of these too. They should be somewhere near an opamp.
Unless it's a potmeter that needs adjusting, you may need the schematic to find out how the low-voltage switching is done and how to modify the threshold.
I've done the same once with a PC power supply, without schematic. Took some reverse engineering, bit of calculating and experimenting, but it worked in the end. Not easy (for me) though.
But ýou may be lucky, in that it is just a potmeter that you can adjust.
BTW, DON'T start turning just about any potmeter you see. Be absolutely sure you've got the correct one, otherwise you will do more damage than good!
Peter,
The Netherlands.