American Airlines Paid Reservation Cancelled, No Recourse Internet

I purchased tickets to St. Thomas in the Caribbean for the Memorial Day weekend.  When I called in to check the status of the flight, 4 days before travelling, I was advised that the reservation was cancelled because they said that I CANCELLED IT.

This was news to me as I had not called them, even though they said I did.  Additionally, no one knew I was travelling so it was impossible for someone that knew me to have pretended to be me and cancel them.  They would not reinstate the tickets.  I am now out $500 for a hotel that I prepaid, and I have to use the $1000 that I paid for the tickets at a later date on the airline that ruined my trip.

American Airlines swears that I cancelled the reservation.  I did not, but there is nothing I can do.  I believe that someone that works for American Airlines wanted to book a friend/relative on the flights, but they were overbooked and cancelled my reservation so they could do it.

I was a loyal AA customer, travelling with them 4-10 times a year, but no more.