Does your car get a good run on the way to work or is it a lot of stop and go, headlights on, other draw on the electrics? BMW's have a really interesting way to shut off non-essential draw. It makes sense that the clock is part of that process.
The battery has an green indicator that should show if it is still good, but in my experience the indicator is only connected to one cell so unless they are all bad or that cell is bad, your best bet it to take it in for a test.
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