Luck seems to play into this more than anything. The phone line folks can't get to the gate agents, so the advice of asking a gate agent to call is good, but nothing beats running. I've had a tight connection go astray because the flight I was trying to catch closed their doors 10 minutes early (as they are allowed). It was particularly sad to make it to the gate with 8 minutes to go and watch the plane sit there with the jet bridge disconnected.