I think I may have found the culprit.
I too suffered from the same issue of the Couatl-menu (and buildings) disappearing once I selected Lihue. The error logs didn't show any error messages, BTW. As far as I can recall, the problem seem to have started with the (standalone) addon manager 2.9.0.5. I waited a bit to see if the (standalone) addon manager that came with Vancouver (2.9.0.6) would change things, but alas this was not to be. I had reinstalled the scenery and the (standalone) addon manager a number of times, even with my AV-software completely shut down (even the firewall) and the folders and "Couatl.exe" excluded from scanning.
So I started looking at files, comparing them to an old backup I had (using Norton Ghost). I stumbled upon the file "__init__.pye", which can be found in "<<your FSX directory>>\fsdreamteam\couatl\Hawaii1". On a hunch, I backed that file up and replaced it with the one from the old backup (I think that one came from addon manager 2.9.0.3, but I'm not sure about that). And lo and behold, the error at Lihue was gone and the Couatl-menu and buildings remained. All other FSDT-sceneries I have currently installed (Hilo, Honolulu and the trial of Vancouver) seem to be unaffected in this regard. After replacing the file, FSX started up a lot quicker, too. I could also choose the parking spot much quicker.
Could it be that a wrong file is included with addon manager 2.9.0.5 and beyond? I have included both files (one as installed by addon manager 2.9.0.6, the other from my backup) for FSDT to examine. I did notice the older file was bigger in size. One thing that might help: I believe the OP is from the Netherlands, as am I. Maybe it is a localized Windows setting (language) that is causing this issue?
Note: I suspect that the old file gets overwritten again when you (re)install another product or the standalone addon manager.