The second unit has kept only 2 hours (!). The behavior is a bit different - the PC sees the disk but no partitions. When trying to initial the hard drive, there were only error messages.
Also WD diagnostic programs (WDFirmwareUpdater.exe, WD Quick Formatter.exe and others) have reported any errors.
Of course I have on different ports (USB2, USB3) on PC (Windows x64, Mainboad: ASUS M4A88TD-V EVO / USB3) and
tried without success to an Acer laptop (Windows 8).
In the support forums of WD there are enough messages to compatibility issues, esp. With USB3 and Renesas USB Controller. However, having such compatibility problems have also Seagate, Toshiba and other manufacturers USB3 disks, and many run WD devices properly. I hope I just had bad luck, and the unit has been "irrevocably" choked on my PC.
I would recommend running more than First a stress test (a lot of data back and herkopieren), also the days on several PC.
Then a hopefully later frustration over data loss remains away.
I have now ordered but a NAS device and will build RAID with a reasonable solution, which also handles other tasks like streaming and private cloud.