The micro-electrode-dot-array (MEDA) architecture provides precise droplet control and real-time sensing in digital microfluidic biochips. Previous work has shown that trapped charge under microelectrodes (MCs) leads to droplets being stuck and failures in fluidic operations. A recent approach utilizes real-time sensing of MC health status, and attempts to avoid degraded electrodes during droplet routing. However, the problem with this solution is that the computational complexity is unacceptable for MEDA biochips of realistic size. Consequently, in this work, we introduce a deep reinforcement learning (DRL)-based approach to bypass degraded electrodes and enhance the reliability of routing. The DRL model utilizes the information of health sensing in real time to proactively reduce the likelihood of charge trapping and avoid using degraded MCs. Simulation results show that our approach provides effective routing strategies for COVID-19 testing protocols. We also validate our DRL-based approach using fabricated prototype biochips. Experimental results show that the developed DRL model completed the routing tasks using a fewer number of clock cycles and shorter total execution time, compared with a baseline routing method. Moreover, our DRL-based approach provides reliable routing strategies even in the presence of degraded electrodes. Our experimental results show that the proposed DRL-based routing is robust to occurrences of electrode faults, as well as increases the lifetime and usability of microfluidic biochips compared to existing strategies.