Somehow Windows 8.1 keeps disconnecting the WD My Passport Hard Drive while using WD Quick View and WD SmartWare.

After reinstalling different versions of the software and the drivers the solution turned out to be a lot simpler: You just have to connect your My Passport with a USB 2.0 port instead of the USB 3.0 one.

The WD SmartWare 1.6.2 works fine, with the newer versions you get Dropbox but the backups seem to hang more often.

Update (2015-04-14):
WD Backup Engine was using a lot of CPU the whole day, even when the external HD was disconnected. The new version WD Smartware 2.4.10 has the option to schedule the backups to once a week or once a day, so the software doesn’t have to monitor your files the whole day. For hourly backups Windows File History is the easier option.