As the locomotion capabilities of quadruped robots are further developed, they are increasingly deployed in more complex environments, heightening the risk of motor failures and significantly impacting their performance. Autonomous adaptation to such failures is crucial to ensure continued operation or safe return. In this paper, we propose a learning-based framework that enables quadruped robots to adapt to single-motor failure and maintain reliable locomotion. Our approach combines a teacher-student framework with a reliability reward term to learn adaptive and robust control policies. The teacher network, which has access to privileged information about motor failures, guides the learning of the student network, which relies solely on a history of proprioceptive observations. The reliability reward term encourages the robot to lift the weak leg to a safe height, mitigating the risks associated with motor failures. We evaluate our framework through extensive simulation experiments, analyzing the adaptability and reliability of the learned policies. The results demonstrate that our approach effectively enhances the robot's ability to maintain stable locomotion under motor failure conditions.