I bought LAX just the other day, Saturday night I think and it worked fine for the few minutes I tested it with the default Jet Ranger.
The next day, I fired up FSX with LAX again and spent about 30 minutes looking around the airport, then switched to night time and looked around more. Everything worked fine and no problems.
A few hours later I returned to FSX, loaded up LAX with the default Ranger again and for some reason all the building were missing this time, except for the jetways. Total mystery since I had already used FSX and LAX a few times already, hadn't made any changes in FSX or on my computer, checked the exe.xml and dll.xml to make sure all the entries were still there, which they were, and also checked Addon Manager while in FSX to make sure it was activated, which it was.
Turned out for some reason, even after FSX has been closed, I opened the task manager and the Couatl process was still running, which after shutting down FSX it usually closes. I manually closed the process, started FSX again and went to LAX and the buildings were back. For some reason I have noticed the once in a while with the latest version of Addon Manager installed, couatl keeps running or doesn't shut down upon the exit of FSX.
Not sure if this is the case with why you guys are having a problem with the buildings disappearing, but I thought I would mention it since the same thing had happened to me and I was able to fix it by closing the Couatl process myself.