I was writing this article where I was testing out how to backup my App Service from the Cloud Shell using BASH. And I got this exception when I was publishing, Figure 1.
Web deployment task failed. (Could not connect to the remote computer ("***.scm.azurewebsites.net"). On the remote computer, make sure that Web Deploy is installed and that the required process ("Web Management Service") is started. Learn more at: http://go.microsoft.com/fwlink/?LinkId=221672#ERROR_DESTINATION_NOT_REACHABLE.)
Figure 1, ERROR_DESTINATION_NOT_REACHABLE publishing using MSDEPLOY Web Deploy from visual studio
Kind of makes sense that trying to publish while the site is being backed up may cause some contention. Regardless, I checked the status of the backup and it was indeed in progress. I waited until the backup was complete, attempted to republish and it worked fine.
Here is some good information abut Web Deploy error codes.