For some reason once I take off after a few minutes the MSFS2020 GSX toolbar icon goes black, turns off, so when I land, I have to open the sim toolbar and click on GSX icon. This happens every flight
That's exactly what is supposed to happen and it's done intentionally.
Because of bugs in the Navdata API and/or issues with the Navdata itself, GSX disables itself while in cruise, to minimize the chance that such issues would cause problems in flights or having GSX not working on arrival because the bugs in the API or the data might have caused Simconnect to get stuck.
For this reasons, even if there's an option to disable GSX in cruise, you might not use it and, since the Navdata API is queried only when opening the menu is opened in flight ( to look for nearby airports ), closing the menu will guarantee no queries to it are being made in flight, until you explicitly open the menu, so the menu is closed intentionally after take off.