Unfortunately Android 4.4 KitKat does restrict file access to the secondary SD card when it comes to writing and deleting files.
This restriction was actually introduced in Android 3.2 HoneyComb but was not enforced by device manufacturers.
With KitKat this seems to have changed (e.g. for Samsung devices) and so File-Managers including DavDrive can not write or delete files on the secondary SD card on some devices.
There is nothing that can be done from a software perspective, the only chance to change this is to root the device.
A detailed description can be found here:
External Blues: Google Has Brought Big Changes To SD Cards In KitKat, And Even Samsung Is Implementing Them
Thanks to Stefan for letting me know about this issue!