See the rest of my explanation: either you have the GSX Verbosity slider too low OR you have set the time interval between messages too high, resulting not getting the message from GSX that is waiting for you to do something before allowing pushback.
Also, try to enable logging in the Troubleshooting section of the GSX Settings page, and ask for pushback. If still doesn't move, exit from the sim, and see if you see anything that looks like an error or a problem in the %APPDATA%\Virtuali\Couatl.LOG file that will be created.
Of course, I assume you are using the latest version of the software. If you are not sure, run the FSDT Live Update now from the Desktop, which will update all your FSDT installed products.