Even though they have a shorter lifespan than other varieties of cells, I would think that 120 days without a nucleus is still quite a long time.
It depends on what you call "to live". RBCs cannot divide, for instance. They cannot synthesise proteins either, so they are decaying after their nucleus is expelled. But they produce ATP using anaerobic glycolysis (as they lack mitochondria), which you may take as a characteristic of "living".