Be sure you allow enough time for the sim to shutdown completely. This can happen several (or many, depending how much overloaded your FSX install is ) seconds later, well after the icon on the taskbar has closed.
You can use the GSX Control Panel while the sim is running, and check the button which says "Waiting for the sim to close", to get an idea how much it takes for the sim to *really* quit and close all the started add-ons.
If you restart FSX when it's still not completely closed, it's likely GSX won't start on the next session, because the Couatl program is still open from the previous session. You can check this on the Task manager: if you still see a Couatl.exe running, Terminate it, so you can restart FSX without restarting Windows.