I am facing this problem when I try to publish my web application on Windows Azure via Visual Studio 2010. I am trying by right click on project and select publish and importing
Make sure you don't have a web debugging proxy running which logs all HTTP(s) traffic between your computer and the Internet. My issue was that Fiddler was running because I was debugging a Web API. I was able to publish successfully after closing Fiddler.
I faced the same problem when trying to deploy to Azure from VS2013 update 5. It happens intermittently. Sometimes publishing works, sometimes it doesn't. In my case it turned out to be network related. We use a load balancing router with two WANs connected to it. If the external IP address changes during the deployment process, because the router switched WANs, it fails. Hope that will help someone.
Same problem here, slightly different solution. I restrict access to the website using the IP. This is done from app services->Networking->Configure Access Restrictions.
My fix was to add the IP to both tabs, the website tab and the scm tab.
try to run Visual Studio as admin. This solved my problem.