These lines in the log:
GSX SimStop
Stopping Application...
Connection with Microsoft Flight Simulator lost (has it crashed?)
Stopping Application...
disconnected from SimConnect.
Seems to indicate that, for some reason, MSFS stopped the Simconnect connection with GSX, which GSX detected as if the sim crashed, so it closed itself as well. Which other add-ons you have that use Simconnect ? FSUIPC or vPilot perhaps ? Some users reported with several add-ons connecting at the same time, the sim might break the connection.