You title is not accurate, because it seems you haven't understood the explanation I gave you in the other thread so, let's do it again:
When I launch "Customize Airport Position", Couatl launches normally and I see the green Couatl icon in my task bar.
Ok, I understand where your confusing came from. You assumed that Couatl started with the editor, because you saw the icon appear in the Taskbar and you assumed it was supposed to exit because the icon disappears. That's not the case, Couatl didn't started at that time and didn't exit at that time, and it was never supposed to "exit". The icon you see is NOT the icon of the program itself, it's the icon of the editor Dialog, which happens to be the same as the Couatl program (because it belongs to it), but it doesn't indicate in any way the running status of the couatl program ITSELF.
The one and only way for you to know if Couatl started ( when starting the sim ) or Exited ( when closing the sim ), is checking the Task Manager, that will tell you about the Couatl program ITSELF.
Couatl is ONLY supposed to start when the sim starts, and it's ONLY supposed to Exit when the sim closes.
After I finish with adjustments I press "Y" to Exit and nothing happens. I remain in the edit mode but no longer in Slew.
So your problem is not the Couatl is not exiting, since at that time is not supposed to exit, but some kind of error must have happened when you pressed the Y key to return to the dialog.
If you have logging enabled in the GSX Settings, exit the sim immediately as soon you see the editor "stuck" the way you describe, and see if there's a log there.