Should I keep this car? I am concerned about low gas mileage and high maintenance costs.
The problem with addressing your concerns is; how much will it cost you to avoid high maintenance costs and high gas bills when you have to subject yourself to big new car monthly payments. Now, your question revolves around selling for what you can and be willing to down size in a more reliable brand while accepting the chance it may not be as a used vehicle. Do the gazintas, look at CR recommendations for reliable economy cars in the acceptable price range and make the decision yourself.
Remember that for the reasons you give, your car is not going to be easy to sell for what you think it’s worth to a lot of buyers with the same opinion. Consider resale before you buy your next in terms of reliability and economy; they trump a lot of other features in car sales.
7 year old Audi? Yup, dump it ASAP if you’re worried about high maintenance costs.
Look towards Mazda for sporty handling and reliability without getting TOO boring(Honda/Toyota)