@droftarts Using new SD cards was not changing anything. I tried 2 others over the weekend. Both are class 10.
As the situation was getting rather worse with the fault ocurring more often, I assumed a faulty SD card reader.
I resoldered the reader with a hot air station as another user reported earlier. That has improved the situation, as the connecton to the SD card seems to be stable for more than 24 hours now.
So thanks for the help and special thanks to the unknown poster with the heat gun hint (sorry can't find the post any longer, so I don't have the name).