I have been suffering from a battery problem for a long time with our gtr r33....If your alarm has its own back up battery it will constantly drain your main battery.....
If the alarm system's battery is down then it will drain and drain your main one until it is full (Most times it just drains it out but never charges itself )
Your best option if there is no mechanical/electrical problem is you just simply have to start your car every two days...and after every use either connect up a tric charger or disconnect the battery....
Hope it helps although this info could not be your problem