Interesting to hear it is a common issue, but rarely have my wife or I had a long commute and this is our seventh BMW and first battery issue; first used car in over fifteen years though.
The build date appears to be 2009-06-05.
After the new battery I'll check the voltage every week and if it looks bad guess I'll look a trickle charger. If it is really is necessary we can tell friends and family we have both a plug-in car and a regular hybrid now
The reason I think the battery is dead is that it likely sat for the last couple of years before I bought it. It is an ex-demo car so had 5K on before sold and then became a company car in Florida just about when real estate bubble popped. It had 10.3K miles on when I bought it and I suspect it sat around unused the company parking lot 'waiting for re-hires when the economy picks up'. I can tell it's an ex-demo car because the warranty lasts until Nov 2013, it was a company car in Florida because that is stated on the Carfax. A few warranty repairs and lack of heated seats aside it still seems like a steal at $31K. The battery is the only remaining issue; assuming it's the root of rough running at start-up.
I can DIY and intend to keep this car around for a long time (it's a 3rd car and they are too expensive for us new!). I shall try to report back if the new battery handles the short commute or not.
Even with many computers this should not happen; modern electronics are incredibly power efficient compared to just ten years ago. Our cell phones have up to 1.5 Ghz processors and operate for many hours on a tiny battery.
Lots of super-rich people buy BMW convertibles as 3rd/4th/6th cars and barely use them, I guarantee most of them would not tolerate trickle charging. My Miata has a tiny battery compared to the BMW and it holds charge fine.
With 4K miles over four years one should expect to have to trickle charge, but not when used daily.
Anyway either the dealer replaces on the next visit or I replace it myself and look into how to register with the car - I saw some software to download on another forum and could try it using an old laptop. Worst case appears I spend ~$200 on a new battery every three years, not the end of the world. Actually trickle charging seems the worst case, won't be super-happy if it comes to that.