From your screenshot you are just editing the default profile provided by GSX, I assume it had already reset on you, and you captured this just as an example.
nevertheless, just to be sure, after you save a new profile does the dialog populate the new profile if you then: save-->close-->reopen?
It should look like the attached example screenshot (substituting the aircraft name for your aircraft), and you should have a directory of that airframe created in:
C:\Users\<localaccount>\AppData\Roaming\virtuali\Airplanes\
with a gsx.cfg file saved containing all your settings.
you can also access this folder just using the %AppData% environmental variable as well.
type: [windows key] + R
in Run Dialog type: %AppData%\virtuali\Airplanes
inside that folder the saved airframe should exist with the gsx.cfg file
