Thanks four your help guys! I am not so sure that it is strictly related to ASE. If it were I would see this behavior at all FSX airports. This problem is isolated to LAX.
The first obvious test would be trying with ASE off. The KLAX AFCAD can't be simpler: all the runways are open both for takeoff and landing so, the runway selection is made by FSX according to its standard scoring methods, where wind has quite a bit of effect, especially if it's significant.
Runways at KLAX are all parallel, long and with enough space between them and with all the ILS aligned to the runway, it's not an airport that would require AFCAD tricks to work so, if anything strange is happening with landings, it should be due to weather.