In my considerable experience I've found that indeed, even a new battery can be discharged so throughly that it cannot be re-activated. This is particularly true of the totally sealed type of battery. The alarm / remote door locking system is always active on this vehicle, so it's inevitable that the battery will go dead after a few weeks storage What you need to do is get a small 1 or 2 amp "battery tender / charger" to use while the car is in storage. That is of course if you have a place to plug it in for 110VAC power. There is also a device, sometimes called an anti-theft switch, which you can put on the battery to totally disconnect the battery from the car. But a beautiful car like your's should be driven and enjoyed often.

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Resistance is Futile.