From your message, it seems that running the FSDT Live Update always fixes the problem.
Assuming your report is correct, and NOTHING related to FSDT appears after some flights ( meaning no Addon manager, no Couatl, no GSX, nothing ), the most likely cause for all of them missing at the same time, is a problem or a conflict with the VC++ runtime libraries.
Since the FSDT Live Update reinstalls them, it's possible ANOTHER add-on you are using is using a different version or an outdated version, or a version that is corrupted in *your* system, so everything using those runtimes will be disabled. But it's very strange it would only happening after the 4th flight.
If, instead, the text of your report is not accurate and, instead, I must believe the SUBJECT of your thread, which is "Couatl won't show sometimes", so you still have the Addon Manager, that's an entirely different issue and, it's usually caused by not having waited enough after the simulator closed to start it again. Yes, even if the P3D Icon has disappeared, depending how many add-ons you have loaded, how free memory you have, it might take a while even *after* the icon has disappeared for the sim to be really safe to be reopened again.
If you want to have a feel how much you should wait on your system, open the GSX Control Panel when the simulator is running, and note how much it takes for the "Compile" button to become available after you close the simulator. That's when it's really safe to restart the sim again. Try the same test using this method.