I would call American Express and dispute the charge. Also, when you called Continental, did they tell you why the change was made, and when it was made? In the end you shouldn't have had to pay, and it sounds like something went wrong with the agents at the airport in Mexico. That would also explain why they didn't call. The res center is not going to call simply because there was a change on the reservation done by the airport. Changes get done all the time, so there's no way to flag those for a phone call.
That's the other reason you need to find out why the change was made - they may have denied the refund if they saw the change was done by the airport agent, and without digging deeper they may be thinking that you had the airport make the change.
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