Further investigations shows that there is a strange damage to the file system of the SD card. It cannot be recognized at all by the mobile, but when I switch off the mobile, remove the SD card and mount it in a USB card reader, it can be read by my Windows PC. I was able to backup everything on the PC, but that is about all that can be done. You cannot delete the contents, not write anything to it, not reformat it, not repartition it and – so far – not repair it. I have tried every option available by Windows as well as several other popular SD-card management softwares. Windows admits that it fails, other softwares “pretend” that they have succeded, but in reality the have not.
I have been able to copy the contents onto another similar SD-card and mount it on the mobile, so everything is now back to normal without data loss, but I have lost a 32 GB SD-card.