the GSX icon turns black and the keyboard command no longer opens the GSX menu. You must click the GSX icon (so that it turns white) to restore the keyboard menu command.
That's exactly what the manual explains about the side-effects of closing the GSX menu from the toolbar, quoting from Page 94:
When the GSX Toolbar icon is Inactive:
• It won’t be able to open the menu automatically when needed.
• No text messages will be shown on screen.
• The GSX Hot-key won’t work.
If you close GSX using the Toolbar icon, making the Icon Inactive again, you’ll have to open it again from the Toolbar before the Hot-key can be reactivated.
This is of course a simulator limitation and, 3rd party add-ons that are supposed to control GSX, should use the full Remote Control (explained in the GSX SDK), where the GSX interface is replicated by them, so you don't have to use the GSX menu anymore.
If the 3rd party program is not made this way, it shouldn't probably close the toolbar menu automatically (if this is what is doing), because it would force you to open it again for the hotkey to work.