According to your post, my understanding is that you could not delete the files in the library using the SkyDrive Pro and Explorer.
I tried to reproduce the issue, the files and folders had been deleted well using the SkyDrive Pro and Open with Explorer, and the files and folders deleted in the library.
Could you delete the files and folder using the UI?
You can check whether the files had been check out.
Some time SharePoint holds a Shortterm lock which is not visible on the UI, you can write a Console App to check if the document is checked out .
If it is ,then, discard the checkout or check in the document (do as needed).
Did the issue occur in other libraries? You can use the other libraries to check whether it works.
If so, maybe the library had been corrupted.
Whats more, you can also check the event log and ULS log to see if anything unexpected occurred.
To check event log, click the Start button and type Event Viewer in the Search box.
For SharePoint 2013, by default, ULS log is at
C:\Program Files\Common Files\Microsoft Shared\Web Server Extensions\15\LOGS
Thanks & Regards,