I have encountered similar problem when the Azure SDK was not updating the Microsoft.Windows.Azure.ServiceClient and Microsoft.Windows.Azure.StorageClient assembly to the latest version in GAC.
Before building the deployment package go to C:\Windows\assembly and make sure Microsoft.Windows.Azure.ServiceClient/StorageClient is version 220.127.116.11 . If the version is 18.104.22.168 the Azure SDK haven`t updated the assemblies in GAC so uninstall the SDK, reinstall it again and restart the computer this will update the assemblies in GAC. After this build the Azure deployment package and the updated assemblies will be part of it.
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