no? your car wouldn't start. If it hasn't got enough power to power a little clock it wouldn't start your car!
If you'd read the OP you should notice it says when he starts his car, (not just the ignition stage, which as you previously said if it was the fuse you speak of, simply switching the ignition on/off would clear the time.) so if the batt has enough to start the car but no reserve then the clock etc will lose info because all avail power is being used.
To the OP:
All fuses should be checked then a new battery fitted and take it from there. Eliminating power source problems and allowing you to continue to the next diagnostic stage.
I have seen a BMW which done odd things with an apparently perfect battery. Used to do funny things including putting all the windows down when starting or coming up with phantom faults. A new battery solved it all. Cars these days rely on computer power very heavily. And we all know computers aren't reliable!
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