The problem This error has caught me more than once, and when you realize what the problem is you understand why. The error you receive is this: >System.InvalidOperationException: Timeout expired. The timeout period elapsed prior to obtaining a connection from the pool. This may have occurred because all pooled connections were in use and max pool size was reached.
Initial thoughts My initial thought was that we were having network issues, and started looking in that direction, which seemed reasonable.
Background Managed or “Smart” backup is a new offering for SQL Server starting in 2014 where you setup a storage device in Azure, setup credentials to that storage device, and then turn it on for the entire server. From that point forward any new database created on the the server, with Full recovery, will do the full and incremental backups, based on the database needs, automatically to your Azure storage.
