Good question Jon,
You can request a interest rate reduction based on the fact that it was not your fault. I recommend you do it in writing and that you do send it certified mail to get their attention. Be very clear about the fact that you had funds available for the automatic draft, but it was not successful through no fault of your own.
If you have had a good payment history in the past, chances are they will reduce your default APR (loansharking rate) back to or close to where it was.
If they insist on keeping your APR at the higher rate, threaten to close the account. That may get their attention better.
If all else fails, transfer the balance with a new card with a lower rate. This forum has a great credit card finder that has over 80 different cards that you can use to compare rates, terms, default APR and all of the other details. The American Express Blue is my top pick with 0% interest for 12 months......
http://www.credit-advice-blog.com/cardoffers.php