Hi JC, i love questions like this. What i would ask you to tell me, is when the alarm activates at night, are you roughly at the same place on the stairs or landing when it happens. When cables are run under carpets, which i personally think is poor practice, it can cause a high resistance in the cable, where it is being walked on over the years. Hence why your alarm is activating.
This may not be the reason, as im only reading what you have written, but i bet im not far wrong.
Regards
Nick 07842 480037 South-East installer and service alarm engineer
Nick
January 2010