Well, I guess there's some solace in knowing that I'm not the only one having problems with American Express these days.
I just went through a very similar situation to the one NJDavid describes. I had sent a payment to Amex for an Optima and it came back unopened and marked "refused." I called and was told to send the payment back, which I immediately did, and they would credit it as on-time. Well, next thing I know my card is being refused. I call again, they say they'll take care of it within an hour. Later that day, my card is refused again.
After many frustrating phone conversations (Them: "Well if you'd sent the payment in on time ...," "I did, you sent it back unopened. This is your fault - not mine.") and a letter to VP of customer service, the matter appears to be resolved (and they even sent me a 45 minute phone card for my troubles - whoopee!)
I spend about $5,000-$8,000 a month with Amex always pay in-full and on-time and have done so for about 6 years. I guess I was wrong in thinking that loyalty deserved some measure of service. I too am looking around for a new primary credit card. Trouble is Optima is free and earns me lots of hotel points ... could they actually be worth the (hopefully) one-time hassle?