In this work, we propose a self-improving artificial intelligence system for enhancing the safety performance of reinforcement learning (RL) based autonomous driving (AD) agents based on black-box verification methods. RL methods have enjoyed popularity among AD applications in recent years. That being said, existing RL algorithms' performance strongly depends on the diversity of training scenarios. Lack of safety-critical scenarios in the training phase might lead to poor generalization performance in real-world driving applications. We propose a novel framework, where the weaknesses of the training set are explored via black-box verification methods. After the discovery of AD failure scenarios, the training of the RL agent is re-initiated to improve the performance of the previously unsafe scenarios. Simulation results show that the proposed approach efficiently discovers such safety failures in RL-based adaptive cruise control (ACC) applications and significantly reduces the number of vehicle collisions through iterative applications of our method.