The problem surely doesn't have anything to do with KLAX, especially considering that, from your video, the fps didn't go down immediately or was in any way related to the loading of the airport (you should see ONLY a single pause when the airport loads, and it should happen at exactly 16.0 NM out, and then nothing ), but it seemed more like a progressive slowdown, which is usually more related to memory exhaustion, so Windows might start to rely on swapping on the hard drive, because there was no more physical memory available.
Of course, this would have caused a 32 bit sim to just crash but on a 64 bit sim, instead of crashing, it will use all available memory, including swapping on the hard drive (even a fast SSD is many times slower than real ram) if there's not enough physical memory.
How much physical memory you have ? Were you at the end of a long flight ? If one of the many addons you are using had a memory leak, this would slowly eat up memory, so you might have ended the physical memory at the end of the flight.
You can use the Task Manager to check how much physical memory you have left under the same conditions.
