Exited the simulator. I've attached the LOG file from. There was NO AI running so can't imagaine it was a sim objects issue and this is at FSDT's own KORD.
Your log doesn't show any errors, and it doesn't show you ever tried opening the menu, but it shows you closed the sim and GSX closed normally after normally receiving your close command so, according to the log, everything is normal.
Are you SURE your GSX is installed in the Addon Manager folder and only LINKED to the Community folder, and you haven't done things like moving the Community folder after installing GSX or manually copying GSX instead of Relinking? Maybe a while ago? Check the two GSX packages in the GSX Community folder: they must be Symbolic links, not real folders, which means they should show a small arrow on their icon.
If you don't have the arrows, it means they are real folders, remove them and then "Relink" with the FSDT Installer.
Hey mate - Addon Manager is installed and linked to the Community Folder. I haven't made any changes to my community folder or even opened MSFS_Addon Linker in weeks.

After the incident above I exited the SIM and went back in and it worked no problems.
Today, I just started the sim up, loaded into KMIA in the PMDG 737 and now getting the same flashing and disappearing menu. Makes no sense. Sometimes it works sometimes it doesn't.
EDIT - Whilst sitting in the sim at KMIA, I've just manually closed COUATL from the menu tray, waited 10 seconds and then manually started it using the desktop icon and am now getting the menu up. It took about 10 seconds for the menu to bring up the options but the GSX menu is appearing again.
Still confused.