I have a 2010 750Li and have the same problems. It started several months ago. The car was jerky and would only drive around 50 mph when I started it cold. I turned it off/on again and the problem sometimes went away. The drivetrain malfunction light turned on. I took it in and they said it was a battery issue. They gave it back to me and said it was fixed. Since getting it back, the power on the car cuts in and out during normal driving, but it is intermittent. I took it in again today and told them do not give it back to me until it is fixed.
Separately, the car has been driving rough from the beginning. It idles like a diesel truck. They changed the fuel injectors about a year ago. It's still rough.