Here are some more results. Now I'm almost sure that this is either a softwer bug or a software correctable one. I removed the battery for the night so that the device would ceompletely power off and the RTC backup battery would run out. When I inserted the battery 6 hours later the thing would just boot up. I switched it on and off several times and it was OK. Then I switched it off once more and when switching on, which I'm not very experienced in , the power led blinked and then nothing happened. I might have released the power button too early, I don't know. I'll investigate this too.

Actually the RTC backup battery seems to have lasted for about 1.5 hours vs 20 minutes as it was suggested here by someone. When I booted up the device showed 6:36 am and I removed the batteries around 5:00 am.