With the ever changing Google Developer UI it is sometimes hard to track where things moved or what functionality is available.
I needed the “Network” tab to preserve the connections even after a redirect and this is indeed possible as per [Wayback/Archive] firebug – Google Developer Tools “Network” Tab clears after redirect – Stack Overflow (thanks [Wayback/Archive] Rodrigo Graça for asking and [Wayback/Archive] Snuffleupagus for answering):
The Wiert Corner - irregular stream of stuff 