The only way to fix it is to reset GSX from the top menu.
That's precisely what that option is there for. Sometimes, depending on your order of operation, GSX might be confused. Which is why we added that option, so you can continue the flight without affecting the sim in any way.
Are you using automatic servicing maybe ? We added that feature because users asked for it, but I think you'll get better control of things you call services yourself.
Then the Ctrl + F12 shortcut does not work and I have to use the alternative top menu.
If the shortcut doesn't work, but the menu option does, it doesn't have anything to do with GSX, it can only be caused by another add-on that has reserved that key, so you must sort out the conflict, either in the other add-on ( if possible ) or from GSX, which has a key mapping feature just for that reason.
Note that, with P3D 5 there's a NEW bug, which cause the menu not responding to keys if the simulator is not in focus and, if the menu is open, it won't respond to keypresses if the menu window itself is not in focus, this was a change in V5.