You see a menu with the latest entries, because the text is saved in a file. The real issue is GSX stopped working or the Couatl engine crashed but, normally, the auto-restarter will restart it automatically.
When restarting Couatl (automatically or manually) doesn't fix a problem, it's nothing related to GSX, it's likely the sim itself got stuck and stopped any communication, this is usually caused by:
Having reached the max Simobject limit during the flight
OR
Issues with the Navdata API or the Navdata itself, which froze the Navdata API which GSX requires when entering an airport. If this is not fixed by restarting Couatl, it's nothing we can do about it, and a restart of the simulator is required.
The second case is usually mitigated if you enable the "Disable GSX in cruise" option, which won't call the Navdata API during the flight ( it's used to make a list of nearby airports in case you want to pre-select a gate in flight ), reducing the number of calls made to the Navdata API and reducing the risk that bugs in the Navdata API or the Navdata itself would cause Simconnect to freeze.