At my place of work all internet traffic is funneled through an Ironport authenticated proxy. If you need to connect to Azure with Powershell through an authenticated proxy (e.g. Ironport) then you need to supply credentials for the proxy to use.
The simplest way I have found to do this on a Windows machine is to include the statement below in your connection script which takes your default cached logon credentials on your local system and populates then into your web proxy credentials.
[System.Net.WebRequest]::DefaultWebProxy.Credentials = [System.Net.CredentialCache]::DefaultCredentials
I got this awesome advice from here:
How can I run an Azure powershell cmdlet through a proxy server with credentials?
After setting the proxy creds you can use either the Add-AzureRmAccount or Login-AzureRMAccount cmdlets in Powershell to “interactively authenticate” and connect to Azure.