Several people have suggested foregoing use of their AmEx cards for awhile, hoping to catch AmEx's attention that way and get some love shown to them. Why not close the account altogether, if the objective is to get their attention.

I haven't used my green card for the longest time (do use SPG one), and haven't been targeted for any great promos, indeed any promos at all. (I trust they would come via email rather than by snail mail, which usually gets tossed unopened.) The only reason I have kept the green card account open and paid the annual fee for it and MR is because I haven't been ready to liquidate the MR account, which one must do before ditching the card, or all those MR points will be lost. (There is the FICO credit consideration too, FWIW, since credit card accounts open for a long time are supposed to help. But does long time mean >15 years, or perhaps just 2 or more?)

If those people with huge AmEx spends (e.g., 100K pa) don't get bid back after they lay off their AmEx cards for months, then I don't know that anyone with substantially lesser spends should expect too much from Amex if they stop using the card.