Best guess is that you are getting a pop up error or configuration dialog from the ODBC connection. If you can't log on as the service account, check the Windows Event Log (Application) for application popup messages at the time of the hang.
The way I explain this is like a phone call. You answer the phone and the user ask you for information. You put them on hold to get the information for them. When you pick the phone up to give them what they want, they have hung up.
This "Request failed (Alternate get): System.Net.HttpListenerException: An operation was attempted on a nonexistent network connection" means that the connection was no longer there, when it tried to reconnect to it.