Similar story to Pakse 2 weekends ago.

I missed my connection from LGA to JFK to take my JFK- SJU flight because the original flight ORD to LGA was 45 min. delayed plus it took an hour to put my luggage on the belt. There were not any other flights to SJU that night. At the beginning AA told me that the only thing they could do for me was to rebook the flight and find me a hotel with a discount (at my own expense). I called the Plat desk. They told me to go to the check in desk and talk to a supervisor. People at that desk in LGA were very friendly and helped me right away. They booked a hotel for me, transportation to the hotel and gave me a $15 voucher for breakfast. The lesson of the story is that you have to keep trying and don't take the first answer as the final answer, specially when it is not your fault.