I was trying to move some Azure SQL databases to another subscription and had issues doing a publish of a SSDT project and also performing a schema compare from Visual Studio 2013. When looking in the error list I saw it had to do with timeouts on the connection.
Updating the connection timeout in the connection properties didn’t resolve the problem.
After googling / binging some more I discovered a StackOverflow post.
Appearantly using a Basic Tier will give you these problems. After scaling up to Standard the issues were resolved. I have yet to find out if you can switch back to Basic after an initial setup of the DB and from there small incremental changes don’t give issues.