If you have an American Express Prepaid Card (not to be confused with Gift Cards), starting October 15 in 2015 they will begin charging a $4.95 monthly fee (except for three states that probably have laws against it (New York, Arkansas, Texas)). You cannot avoid the monthly fee no matter what. The easiest way to deal with this is to use up your remaining balance before the new fees arrive. Screenshot of the relevant parts of the email below:

The reason they are doing this is likely because they recently launched a new prepaid option, the American Express Serve, which has more benefits than the Prepaid but it’s a different card and you have to apply for it separately.

If you have a card, you may have received an email from them outlining this transition. The email also mentions an offer that encourages customers to apply for the new Serve card: get a $25 account credit if you spend $25 or more with a new Serve account.