Even though this may not apply in your case: Could the reason for the fault being that someone (maybe you) tried to connect a too large (in Watt) power supply which overloads the curcuit and causes an automatic shutdown. I have had this problem with my Dell Latitude D820.
I think that one problem is charging the battery and running the computer at the same time. I am considering to bring an extra power supply with lower wattage on the next trip as my laptop will run and charge using this PSU but will display a message that it is running on reduced speed.
Well, if this is the case (removing the battery), then the staff at SAS have no idea. The thing that peeved me off is that they advertise this as one of the main reasons for choosing econ extra over econ. The fact that only some seats have this should be stated.
I have travelled in SAS econ extra CPH-PEK before and had no problems. Also no problems with LX C class. I think that the problem lies with the plane's electrics.