The only time I become tired of playing a FPS game is when I'm playing it for multiple hours.
It's not just FPS games; you can say that about any game or any product. You can only sustain enjoyment of something for so long before you grow increasingly tired of it. There's a common rule of economics called the Law of Diminishing Returns, and it goes something like this:
When you first get it, you're happy. You expose yourself to it more and become more invested (the first X on the graph). After a certain amount of time has passed, you begin to feel like you've seen it all before. It becomes predictable and you lose interest (the second X on the graph). Then you put it away for a while.