I wouldn't leave a car for 17 days without the hotel being aware.

A few airport hotels have parking packages of different durations, but most just do the seven day deal. Some have policies of very reasonable surcharges if you need an additional week, etc., as policy but it's not posted this way as an official rate. For example, a place (not SPG) where I sometimes stay with an airport parking rate charges $25 for an additional week but tends not to fuss or bother charging me if the car's stay exceeds a week by not very much. ADDED: They also seem willing to give me a parking package by just adding the parking fee, even if their website isn't offering parking package availability for the night I need to stay. Finally, at another airport hotel I've seen people park their cars and use the airport shuttle apparently in exchange for just paying the parking price, with no overnight stay required, although these people might be regulars or otherwise have some inside connection.