My United Airlines flight out of Miami was delayed due to mechanical problems. I was assured that my connection to my final destination would not be in jeopardy. I raced to the gate only to be met by the United agent telling me that they would not let me board. BTW, my luggage made it on the flight. I was not the only one: the gate agent was obstinate and confrontational with another passenger that was delayed on my flight. I tested their disposition by asking would they mind comping me a meal at the airport for the inconvenience. Naturally it was 'no' and United Airlines has lost my business forever. It's been 4+ years and I have not boarded a UA flight.
What responsibility do airlines have to accommodate delayed passengers when their own flights are only slightly delayed? (i.e. bags make the transfer)
For example: In my experience US Airways will radio the connecting flight to ask the connecting flight's captain to hold in order to enable his passengers to make their connection.