Airline mile rewards credit cards are a great way of earning airline miles but those high annual fees that come with these cards can be a little hard to deal with. Many credit card companies will waive the fee for the first year but after that you will be stuck paying them. If you cancel your credit card it can negatively effect your credit score so you could ask to "down grade" your credit card to a fee free card which won't effect your credit score.
However you won't earn miles with these fee free cards so if you want to keep the card you have you could call in just before the annual fee will be coming due and ask if there is anyway they could waive that fee for you, pointing out what a loyal customer you are and how you pay your bill every month on time. There is a chance they will say they can't waive the fee. Which is exactly what I have been told many times. I just hang up and call back, this time asking to speak to a manager. I explain to the manager that I am a loyal customer, making charges to my card every month and paying my card on time each month and ask them if there is anything they can do about the annual fees for me. The don't "waive" the fee but will credit my account the amount of the fee.
So as long as you maintain a good credit history with the credit card company that will give you some pull with them and they will be willing to work with you. Never be afraid to ask for what you want, just remember to be polite and courteous.