Note that BA has a specific warning for CPAP noting that one should nonetheless use or have available an appropriate dry cell battery in case the power point is not working.

While the suggestion in #11 is a good one, simply recycling the system may or may not work. Passenger power points are not on the MEL list for the UK (or US), so if non-functioning, BA would not likely delay the flight and if inflight, not any action to take.