The G3X Touch used in our Hawk is one of the default GPS options included in MSFS, developed by Working Title, so we don't actually have any control over its functionality.
The logic of the flight plan being removed when the GPS is turned off, I can only assume, is either accurate to the real unit or is a feature that has been implemented for MSFS compatibility.
I seem to recall that in order to get a flight plan loaded in the G3X that you have to have departure and arrival airports entered in the flight plan. So if you try and create a flight plan when the aircraft is not on the ground at the departure airport, the GPS may not create the flight plan.
Mark - Just Flight