Ken
You have not given us enough information to really understand your issue or to suggest an effective solution. From the title of the question I assume that you are running BGP. So one of the first questions would be if the BGP neighbor relationship came back up and is established when the T3 came up? Are there Verizon routes in the BGP table? Are there Verizon routes in the IP routing table?
It would also be helpful to understand how you are configuring it so that the T3 is the primary connection. Perhaps something there is not re-setting as you expect. Posting the configuration would help to answer this part of the question.
HTH
Rick
HTH
Rick
