The sensitivity of millimeter wave (mmWave) signals to blockages is a fundamental challenge for mobile mmWave communication systems. The sudden blockage of the line-of-sight (LOS) link between the base station and the mobile user normally leads to disconnecting the communication session, which highly impacts the system reliability. Further, reconnecting the user to another LOS base station incurs high beam training overhead and critical latency problems. In this paper, we leverage machine learning tools and propose a novel solution for these reliability and latency challenges in mmWave MIMO systems. In the developed solution, the base stations learn how to predict that a certain link will experience blockage in the next few time frames using their past observations of adopted beamforming vectors. This allows the serving base station to proactively hand-over the user to another base station with a highly probable LOS link. Simulation results show that the developed deep learning based strategy successfully predicts blockage/hand-off in close to 95% of the times. This reduces the probability of communication session disconnection, which ensures high reliability and low latency in mobile mmWave systems.