Asp.net-mvc – A network-releated or instance-specific error occurred while establishing a connection to SQL Server

I have a simple mvc web site (using the VS internet template) on azurewebsites talking to a SQL Azure database in the same data center. The database at this time is just to do the built-in SimpleMembership Provider. I have already switched from the default App_Data mdf file to Azure SQL. It works fine, but sometimes after a while, it would give:

A network-related or instance-specific error occurred while
establishing a connection to SQL Server. The server was not found or
was not accessible. Verify that the instance name is correct and that
SQL Server is configured to allow remote connections. (provider: SQL
Network Interfaces, error: 26 – Error Locating Server/Instance
Specified)

with a long message:

SQLExpress database file auto-creation error:

The connection string specifies a local Sql Server Express instance
using a database location within the application's App_Data directory.
The provider attempted to automatically create the application
services database because the provider determined that the database
does not exist. The following configuration requirements are necessary
to successfully check for existence of the application services
database and automatically create the application services database:

But I do not have a connection string using SQL Server Express!

Restarting the web site immediately does not remove the error.

Without changing anything and restarting the web site 15 minutes later give:

502 – Web server received an invalid response while acting as a
gateway or proxy server.

There is a problem with the page you are looking for, and it cannot be
displayed. When the Web server (while acting as a gateway or proxy)
contacted the upstream content server, it received an invalid response
from the content server.

Previously, I could restore the website back to working order by just re-publshing from VS. But for the last hour I have tried and tried and I cannot get the web site to work again.

What is the problem about SQL Server Express really about?

My connection string section contains:

<connectionStrings>
  <add name="DefaultConnection" connectionString="Server=tcp:sabl6h4---.database.windows.net,1433;Database=MVC;User ID=test@sabl6h4---;Password=----;Trusted_Connection=False;Encrypt=True;Connection Timeout=30;" providerName="System.Data.SqlClient" />
  <add name="Entities" connectionString="metadata=res://*/Data.Model1.csdl|res://*/Data.Model1.ssdl|res://*/Data.Model1.msl;provider=System.Data.SqlClient;provider connection string=&quot;data source=sabl6h4---.database.windows.net;initial catalog=MVC;user id=test;password=----;MultipleActiveResultSets=True;App=EntityFramework&quot;" providerName="System.Data.EntityClient" />
 </connectionStrings>

Just to be sure, I copied and pasted sabl6h4—.database.windows.net into SSMS and connected using login test and it opened the database without problem.

One day later: I created a new azurewebsite and published the exact same project and same web.config. It works fine without problems. After some minutes, the exact same error occurred!

Three more hours later: Went for lunch, came back, hit the browser Refresh button, and the web site is up again. I am convinced that someone is fooling around with the settings at the back end.