Would've helped if you'd've named the card in question. Lacking that information., here's a generic answer. Annual fee waivers are the crown jewels of retention offers. Always try for them, but don't make that an all-or-nothing goal. As a fallback, ask for points/miles and/or a challenge to obtain same. Ask if they can help you in any other way. Ask to talk to a supervisor. Always be polite. Rinse and repeat. Lastly, while there may be an offers "system," there is always the possibility of an offer outside the system. That's why you want to include talking to a supervisor in your approach.

RNE, a graduate of the George W. Bush School of Strategry. Super-duper cum laude.