I'm not a car guy, but I believe that a car's ability to hold time while off relies on the "engine off" current. If you have a problem with any of the parts or fuses in that circuit, your car will not be able to remember what time it is when the car is turned off.
This might make sense if the car is reliably able to start.
That being said, I just replaced my Toyota Matrix battery after 7 years, as the battery was only holding a partial charge.
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