I got two platinum-level AAdvantage cards (one Visa, one Amex) back in late 2012. In 2013 and 2014, I got retention offers of statement fee credits plus 1000 bonus miles for every statement I spent at least $1000 for each of the two cards. It's been a good run, but I guess my luck finally ran out (relatively speaking).
A few nights ago, I talked to a woman with a bit of an accent (turns out she was in Costa Rica). She only offered to perform a product change on the cards to no-fee cards. I downgraded the Amex to a Citi AAdvantage card that only gets one mile for every $2 spent. I doubt I will ever use this. I changed the Visa to a Double Cash card, which isn't bad at all for non-bonus spend (2% back).
I still have two legacy Barclay USAirways (now Aviator Red) cards that each refund me 10K miles every year that I pay the $89 anniversary fee, and give me a free bag, earlyish boarding, etc, so there wasn't much point in keeping the platinum-level Citi cards.