Official corporate policy changed recently (within the last few years), and I can't remember the specifics (I get the old and new ones mixed up). But depending on where you are renting, it varies anywhere from two to six hours. After that, your reservation is effectively canceled. You do need to change your pickup time in order to guarantee availability. If doing so online results in a rate change, try calling the location directly and asking to change the time. If you can't get the direct number to the location, try calling the main reservaitons line and asking for a manual pricing override (ask for a supervisor if necessary).

I would not suggest simply showing up later without making arrangements ahead of time. I have seen many people turned away from the counter without a car in exactly the same situation.