As previously mentioned, AMEX gift cards do carry a monthly maintenance fee. Many other gift cards have a monthly maintenance fee as well, but these often do not come into effect until a pre-defined period of account inactivity.
Modern-day gift cards aren't like the gift certificates of years past. They're essentially debit cards - usually you can add balance to them. Account maintenance fees are just that - since, unlike a gift certificate, it does not have a plainly stated face value but an electronically stored value linked to an account number stored in some database somewhere, there are overhead expenses. Maintenance fees recoup those expenses.
Unintended consequence of the success of consumer advocacy groups who lobbied to make gift certificate expiration dates illegal.