A recent story we can all learn from:
I got this offer to upgrade my gold to plat for 25k but when I tried to upgrade, it said I was not eligible.
Called cs, they opened a case and sent to back office.
Called a few days later, was told there's now a note in account saying I'm not eligible, would have to wait for correspondence by mail from back office to pursue further.
Tweeted askamex. Got a response with a link to send an email through my account. Got the following unhelpful response:
"Please call the customer service number on the back of your card, they will be able to help. -Dre"
Called executive office number, could not get through to The Man but got his email. Sent an email to chairmansoffice@aexp.com with no response yet.
Called the number provided in the email, was bounced around from Kansas to India and back to Tennessee (or maybe still India) and got a guy who either didn't see, or didn't have access to, the note in my account saying I was ineligible. Upgraded my card without a problem.
Lesson: With Amex there are many Avenues. Try them all and you shall succeed.