Suggestions on how to get creditor to waive this late fee?

[Auditmaster]

I have a American Express Bluecard. I have had many cards over the years and have never had a late payment or went over my credit limit. In fact, I have always paid my balance due way before the due date on all my cards. I realized that I was approaching my credit limit on the card, but thought that if any particular charge was going to exceed my credit limit, it would simply be denied and I would have to find another way to pay. Wrong! I was allowed to exceed the credit limit (This one was only over by $1.50), but was charged a $29.00 fee. Owwwch!

I called customer service and asked for a one-time waiver and they said "no way". Of course this is my mistake - I was just unaware about what would happen if I ran up against my credit limit. But I know many businesses will waive a charge for a one-time mistake to keep you as a customer. I was going to write a letter or email asking once again for a waiver, and threatening to close my accounts if they refuse. Anyone have any idea if this will work or other suggestions about what to do? Thank you in advance for your time!