I'm with Kate_Canuck on this one.

Find out what their complaints proceedure is and follow it though (in writing, using recorded delivery). Don't speak to people on the phone, you might as well talk to a brick wall because there is no record of the call (Amex will record it but you probably can't) so they can say anything and deny it later on.

If they don't agree to honour the contract then take it to the ombudsman. If nothing else, it costs them a fair amount of money to defend the case and they will probably settle with an ex-gracia payment before it comes to this.