I usually call after the fee posts (when I receive the statement showing that the annual fee has hit). I would suggest this because there have recently been comments that AmEx might claw back the bonus you received on the card if you cancel before the one year point.
I agree with the advice above. After the fee hits, call to see if you get a retention offer. If you like this card, and prefer to keep it if you can get an offer, I would also consider if it is worthwhile to put some spend on the card now. I tend to think that the credit card companies look at how good a customer you are when you threaten to cancel.
If you have enough time before you have to make that keep or cancel decision, both the Everyday card and the Blue for Business Plus card are Membership Rewards cards with no annual fee. I have had the ED card for a while, which allowed me to keep my MR points when I cancelled the AmEx Plat (I was not offered a retention bonus). The Blue for Business Plus card is a newer product that I picked up more recently. I don't know if you can downgrade a Gold card to one of these (possibly not), but I am suggesting that you think about a separate app for a new account.
