My husband's flight #1886 from SFO was delayed 40 minutes from SFO to Miami (no weather problems, just stupidity apparently) so when he landed he only had 10 minutes to get to his second connecting flight (AA made the connections that close) over a mile away from where he was in a different terminal.
I called the airline to try and get the plane to hold and the connecting flight knew that there were 10 people (besides my husband) from this delayed flight running to the plane (Flight 1051). When everyone got there, the plane was there but no one at the gate would let them on. My husband was told to go to customer service, which he did away from the gate since no one on the second flight would let them on.
While at the customer service desk the lady informed him that "there are mechanical issues, Flight 1051 is now delayed and they are letting people on" the customer service rep radioed the desk at the gate to let them know that my husband was en route back to the gate and when he got there they shut the door in his face and said "tough" even they all knew at the gate that my husband was heading back there. I have tried to talk to customer service online via their site, on the phone, via Twitter and FB. American really could care less about their passengers. So wish there was something more I could do.