I contacted reservation reps from Alamo, Avis, Budget, Dollar, Enterprise, Hertz, National and Thrifty and posed your question.
Without exception, each told me the the amount of time can really depend on the particular airport car rental company that you have a reservation with. The amount of time allowed can vary from under an hour to six hours or more -- depending on the location and company.
Off airport locations tend to be different as well. The rental can be held for a few hours, or for some companies they will hold the rental only until the regular closing time of that particular location.
I was told that when determining how long does the rental car company hold the reservation, the answer will vary by location.
Most airport car rental companies ask for a flight number when you make your reservation. This allows them to calculate the approximate pickup time (based on the flight arrival, time for luggage pickup as well as the amount of time it generally takes to get from arrivals to the rental counter -- whether you must go on foot or be transported by shuttle. Having the airline and flight number on a reservation also allows the car rental company to keep track if your flight is delayed.
The reservation reps all told me that in order for you to get a specific answer to how long does the rental car company hold the reservation, you should contact the rental counter of the specific rental company you're using at the airport you're renting from; this way you can be sure of the policy of the particular car rental company you're renting from.
This is especially important to do if the company has limited hours of operation (ie not open 24 hours a day) and your flight arrival is either close to closing time or close to midnight (which if you were late, would push your rental into the next calendar day).
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