Drew has it right. The airport has nothing to do with the car rentals. They're a convenience for the travelling public. Kinda like the TSA doesn't get cheap tickets. All are there, but not the same. Robert's field closed for ywo days last winter because of system failure. Other than that, they're open from 0400 to 2300 every day.
It's possible the rental car business you're attempting to rent from is just sold out of cars those dates. The airport is open, especially if you have tickets. Try other rental car businesses. They have Hertz, Enterprise, Alamo, Budget and Avis right inside the airport.
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