In recent years, with the development of Internet of Things (IoT) technology, Internet of Vehicles (IoV) has become a key trend in the automotive industry. However, challenges remain, especially in the authentication of new vehicles and roadside units (RSUs), including data privacy, security, and interruptions caused by high vehicle speed or RSU confirmation delays across blocks. To address this, we propose a method based on blockchain and reinforcement learning (RL). Leveraging the decentralized, distributed, and tamper-proof nature of blockchain, a nearby vehicle moving in the same direction as the disconnected one is selected as a relay mining node to complete the interrupted authentication process. By modeling ledger grouping and scheduling with a Markov decision process, we establish a feasible system model to solve the disconnection issue. Simulation results demonstrate that the proposed solution effectively handles vehicle authentication interruptions, significantly improves verification efficiency, and ensures privacy and security throughout the process.