I now would say there is definitely something wrong with power consumption!
I charged my device (an X) and kept it in flight mode over a day and night and it consumed 3% only. So far so good
Then in the morning I disabled flight mode, so network and WLAN were connected. I did not use it and in the late afternoon it was already down to 50%. I then disabled WLAN for some hours and consumption was about 1% only.
After that I enabled flight mode again but enabled WLAN. And power consumption is 3-4% per hour with null usage.
So WLAN connected with no usage at all drains the battery! 