but upon leaving FSX, GSX reverts to trial mode.
You mean after restarting the sim from a previous session, you find GSX is in Trial ? If yes, it might be simply because you restarted the sim too quickly without allowing for all open files and process to close and this, depending on your settings, your memory and your add-ons, can take a while, even long after the FSX icon has disappeared.
Try after a Window restart and, the next time, check the GSX Control Panel, and see how much it takes on your system for the "Compile" button to become available. This is when it's safe to restart FSX again.