In order for emails to be sent out to the internet, there must be an "Email Access" rule that matches.  Yes, even for yourself.  This is a security measure to prevent people from sending you carefully crafted messages that get sent to the internet without your knowing.

To add an email access rule, go to Preferences and choose Email Access.  Create a new rule and put your callsign (exactly as it is configured in the User portion of preferences).  Leave the type set to Both and leave the Email Filter box blank.

Once you do this, you should see emails leave your Outbox periodically and when you click Send/Receive, assuming you have Automatically Forward Messages enabled in the Messages portion of Preferences.