Not sure how long it stays in the system, but you can do a couple things. Call Thrifty and ask them what would happen if you got in later, don't have to tell them you are changing flights, just ask what happens if you got their 5 hours late? Peoples flights are delayed all the time, so my feeling would be it stays for a while in the system. You could always do a mock booking on line and see what the new rate would change to, if any change at all. You also have to watch out for things such as if you rented on a special weekend rate. That might require you might have to pick up the car say between noon Thur and noon Fri and not drop it off before say 6am Monday. If you picked it up after noon on Fri you may loose the rate and have to pay by the day.
Let us know what they say, I'm sure there are others interested