This has happened to me so many times on all airlines. Often due to mechanical delays. Once on US Air was at the gate about 25 minutes before departure, they already gave the seats away. On Delta we had originally about a 2 hour connection, 7 of us got at the gate about 9 minutes before departure, and we stood there for another 15 minutes watching as they loaded our luggage on the plane. Often on a late flight the agents of all airlines just take their good old time in dispatching the plane. More important than reporting on-time departures, airlines should report misconnects. If airlines were required to report mis-connected passengers, you would see how quickly they start holding flights to a city that is an end destination with a good amount of time to turn the flight around so that the delay does not ripple.

Airlines just want to get the door closed, even though it will be at least 15 minutes before push-back.