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the problem is not the battery
the problem is that you have a parasitic draw. This is actually somewhat common and your dealer should have been able to resolve this easily with some testing.
There is some component on your vehicle that is draining power overnight while the car is supposed to be off.
If you have any kind of aftermarket equipment installed (GPS, ipod dock, etc), this is the first suspect.
If there is no aftermarket equipment installed, the blower motor controller is by far the most likely culprit. Also, the electric engine fan is also somewhat common.
Beyond these items though, it could be ANY component on the car.
In order to determine the cause of this, you will need to unhook the negative battery cable and hook up an amp meter and measure draw after the car is locked and has sat untouched for 20min (this is when it is supposed to be in "sleep mode"). If there is more than about 50ma of draw at this point, you will need to pull fuses one by one until the draw stops. Whichever fuse stops the draw is the problem circuit.
If you are not familiar with using this equipment or performing this type of test, you should have it carried out professionally, any BMW specialist or auto electrician will be familiar with this testing.
BMW dealers also have special equipment they can use to help identify the cause of this, so this is a second option, besides the above test.
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