[Suzuran]

It's a match-criteria-based list, so you stay at the top until you die or receive a matching transplant. If you are at the top of the list but don't match an available organ, the organ goes down the list to the highest match that can be brought to an operating room in time.

Edit: Geography is important too. The kidney can only survive outside of a (cardiovascularly-functioning) body for minutes at a time. If you are at the top of a list but the kidney is across the country and you don't have access to a private jet, it's going to someone else. This is the "loophole" that Steve Jobs used to get a liver transplant - Since he had a fleet of private jets available to him, he could be simultaneously listed for transplant on multiple lists.