I'm going to admit right now that probability and statistics are not my favorite things to work on. That being said, I'll give this one a shot.
My answer is that the contract will be renewed 3 times. The way I'm working the math is that it's an 80% chance the contract will be renewed once, a 64% (.8*.8) chance the contract will be renewed a second time, a 51% (.8*.8*.8) the contract will be renewed a third time, and a 41% (.8*.8*.8*.8) the contract would be renewed a fourth time. At that point the chances are less than 50-50, so it likely would not be renewed.