Mine battery was replaced under warranty yes, but it said right on the paperwork that the computer is saying "unfavorable driving profile, too many short trips". And I never cycle the top without the engine running, specifically to avoid hitting the battery too hard knowing that I do a lot of short trips.
2012 E70 X5d (IT'S HERE!) Deep Sea Blue / Sand Beige, Premium, 3rd Row, Multi-Contour
2011 E93 335i Deep Sea Blue / Oyster, Step, Premium, Convenience (PDC & CA), and that's it