Firstly, batteries are never filled with mineral water, let alone mineral oil. They are filled with distilled water, which takes the minerals out, unless you have very soft water locally, in which case you can use tap water. Neither is required, though, if the battery electrolyte level is where it should be.

Call your dealer and ask if your plan covers the battery. No reason not to let them do it if it does. They would check your charging system at the same time.

Also, you may have something draining the battery. Dealers do a current draw test to make sure the vehicle is going to sleep. If something is preventing it from doing so, whether it is the FSR or something else, you will continue to get flat batteries, even if you replace it.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue