Range Rover 2005 Flat Battery !!!!

[marinesparks]

Im currently looking at a friends 2005 range rover vogue that has the dreaded battery going flat syndrome,,,
today we checked the rf box fitted on the o/s rear but its a later one that thats not suposed to have the problems discussed on here before, but the single cable that is suposed to be attached to the window has come away from the glass contact, if this is loose and with heat changes could this also cause strange signals causing the Becm to wake up as the old units caused ?

Also checked the alternator this seems to be fine other than the battery being a little low 12.11 volts when we started the engine, once started the alternator charges at around 14 .3 volts with 120 amps dropping to around 55 amps after about 10 minutes of running, the problem being when you turn on the heated front screen / rear screen / lights and air con the amp rate goes up again which i would aexpect but the voltage gradually decreases down to around 12.5 volts, is this cause for concern. Ive asked the owner to put the battery on charge over night as it has been sat for 2 weeks unused and had to jump start it start it just before i got there today. The eye on the battery shows green just about,,,

Also is the final stage resistor on the 2005 model still an issue causing the Becm to wake up as before ? and if so is the a way of testing the resistor ?

ANY HELP WOULD BE GREAT PLEASE,,,,,,,,