Deploy sample server based on IT Hit WebDAV Server on Azure website. You can deploy either NtfsStorage Example or SQLStorage Example, described here:
Understand why IT Hit WebDAV is not functioning. Find out why logging is not working (WebDAVLog.txt not created).
Provide design recommendations what needs to be changed to make it work with Azure.
You can download a fully functional IT Hit WebDAV Server Engine and samples here:
I will provide more details and instructions about this and other tasks and projects during communication.