How long does the connection last for exactly? If I were a betting man, I would say it's failing after exactly 2 minutes, which would correspond to the default timeout period many systems have.
Is both consoles on the same subnet? Are you going through any routers or L3 switches between consoles? Something is likely letting the initial connection though, but then not sensing it being used for some reason and cutting it off after a timeout period.
-Eric Kincl