Could it be that GSX takes the Window focus and doesn't release it (only guessing)
No, it doesn't.
The only time GSX takes the focus, is when you open the Settings menu, the scenery configuration editor or the airplane configuration editor (and of course it releases it correctly, otherwise you couldn't use ANY of the FSX keys, if FSX lost the focus), not the in-game CTRL+F12 menu, but nobody is reporting this issue in relationship with these menus, they all say is fixed by opening closing the CTRL+F12 menu. And that menu is handled by FSX itself.
In fact, you can do a very easy check, which will confirm the problem is not GSX:
- Open the GSX CTRL+F12 menu
- While the menu is still open, use a default FSX keyboard command, like S to change view. It will work.
This clearly indicate there's no focus problem, GSX doesn't takes anything, and FSX is perfectly able to process keys with the GSX menu open. Which is not even a "GSX menu". It's a standard FSX Simconnect menu, created and handled by FSX itself, GSX will only indicate the title and the items, but it will not try to handle any keys directly.