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I recently received a retention offer on one of my Amex cards.
The annual fee on another of my cards is coming up soon.
Would it be considered bad form to ask for a retention offer on that one as well?
No
You should be able to ask for offers on each, but it's not guaranteed that you'll have an offer
I think it's every 13 months minimum you can get an offer per card, so you can usually try successfully every other year per card