You've had Amex cards for many years and never been late, funneled huge amounts of money to them, you paid one day late one time and they won't give you a courtesy credit? That would be my sign to end that relationship.

I actually closed out my Amex cards a year ago because the service every time I called in was terrible, and the cards didn't actually offer me anything (rewards or otherwise) that I couldn't get somewhere else.

It's really rather shocking that they still have a reputation as being a high-end, service-oriented brand. No joke, Discover has far better customer service than Amex (no dig at Discover - they're legitimately good; it's just that they often get dismissed out of hand).