From the Prosine 2.0 Manual;
Page 77 of 148Inverter Low Voltage Shutdown:
At or below this battery voltage, the inverter will shut down.
The values range from 10–16Vdc.Inverter Low V Warning:
This is an offset voltage
ranging from 0 to 3.0V. When the battery voltage drops
below the sum of Low V Shutdown and Low V Warning, the PROsine will sound a warning.
Inverter Low V Restart Hysteresis:
This is an offset voltage ranging from 0.5 to 2.5V. When the unit has shut down
due to low battery voltage it will not automatically restart until the battery voltage recovers to the sum of Inverter Low V Shutdown and Inverter Low V Restart Hysteresis. When the PROsine shuts down the battery voltage will rise and may cause the PROsine to restart, which drops the voltage again so the PROsine shuts down, etc. This hysteresis setting reduces this problem. The default value is 2.5V and should not be changed unless there is a special reason for doing so or this problem will return.
... have you checked these settings?