A complete de-installation & a complete re-installation have not been successful. Not even the installation via the Offline Manager... The "Run as administrator" setting was also unsuccessful.
Of course a reinstall couldn't fix it, because your problem doesn't have anything to do with GSX, and it's caused by something interfering with writing in YOUR OWN user profile folder, something that is normally impossible, since you should always have permission to write into your own profile folder.
The most likely cause is the antivirus interfering so, first of all, configure the antivirus to add the whole "Addon Manager" folder to the antivirus EXCLUSIONS, then run the FSDT Live Update again.
If that still doesn't work, remove this folder:
%APPDATA%\Virtuali
And reinstall GSX again. Note that, doing this will remove ALL your preferences and all your custom airports and airplane profile, so if you have any, you might to MOVE the "Airplanes" and "GSX" folders there to a different location before removing the main %APPDATA%\Virtuali folder, and restore them in the same place AFTER reinstalling.
Reinstallation is required, because the installer will need to setup the correct permissions to all folders.