Yes you will have to call back every year to ask for a AF rebate/waiver or ask to transfer to card to a AA Bronze card next year (or after) which does not have an annual fee. This would keep your credit line available for emergency use.

The Bronze card only rewards half the miles as the Platinum/Gold cards so no reason for you to do this until if/when Citi refuses to waive (or rebate) the AF of your Gold card.