I recently had this problem with my 2013 R56. I needed a replacement vacuum sensor. My battery was fine.
The sensor was, if I remember correctly, £125!!!!!
the eobd system is very much designed to try and protect the car if one thing dont work correctly, and switches off some feature like start stop and dpf regen.. its the trouble with these new tech cars the eobd system was meant to make things easy when reality is without dealer level diagnostics and live data runs and knowing what the numbers should be is very hard to pin point what has gone wrong, as the key question is always is the code the product of the sensor it points to or a bi-product of a completely different fault,
i had a map sensor implausibility fault a while ago for boost pressure on a turbo car,, checked the wiring the live data nothing sprung out, ended up being oil pump failure or gone weak 15psi oil pressure at 3k not good and the turbo bearing would not float and caused drag in the bearing and then turbo failure about 500 miles later,, the map sensor was doing ot job telling us low boost ie under boost,
bit same as dpf faults can be any fault code in the ecu will stop the regen and cause even bigger issues,, so important that people as soon as get a warning go get it looked at could save thousands if turbo fails due to the dpf blocking cause a diesel runaway that destroys the engine totally,, seen this a lot of times,