This morning AmEx sent out an email stating that on January 6, 2016, they will start charging a $4.95 monthly fee to Amex Serve Softcard accounts. The notice did specifically say Softcard account holders so I am not sure if this also applies to regular Serve accounts.
"Starting on January 6, 2016, there will be a $4.95 Monthly Fee for your American Express Serve Softcard Account. This fee will be waived if you Direct Deposit money onto your Account during a monthly statement period."
The monthly fee can be waived if you have a direct deposit coming into the account. I have an Alliant account whose ACH transfers have a good track record of counting as a direct deposit so that's the first method I'll be trying.
Fortunately, Amex has not turned off the free money faucet for depositing via credit cards yet. Here's to milking that for as long as possible.