But sometimes when I end a flight,FSX crashes and then the next time I start a flight,the Couati menu is missing again.
Your issue is not that Couatl disappears. Your issue is that FSX crashes after a flight. This is not normal, and it's not obviously caused by Couatl, since Couatl (being an external .exe) cannot crash FSX, since it doesn't have any control on the FSX memory areas. Only a .DLL module has the ability to crash the sim.
But the abrubt crash, caused by something else, MIGHT result in Couatl.exe still running, because it might have not received the notification from FSX to close (maybe FSX crashed before being able to send it), so it's possible you still have Couatl.exe running in the background after the crash.
You might think the problem is "fixed" by reinstalling it, but that's just because the installer will terminate any running Couatl.exe automatically when it starts.
The next time FSX crashes, check with the Task Manager if you still have a Couatl.exe running, and Terminate it, so this should fix the next startup.
Of course, you might want to check WHY FSX crashes after a flight, which is the real issue, and Couatl it's just a victim of it