In vehicle-to-infrastructure (V2I) communications, various failures in the dynamic movement pose serious link interruptions. To study the continuous service quality for the V2I network when this issue happens, this paper proposes a survivability analysis and establishes the communication architecture for software-defined network (SDN)-based V2I communications. With the controllable advantages of SDN centralized management, the multi-path transmission control protocol is used to seamlessly switch the transmission information between the V2I links of each vehicle node. Specifically, according to the analysis of specific fault types for V2I links, the definitions of SDN-based V2I survivability is provided to establish the corresponding survivability mode. To further verify the survivability model, a full-state search is adopted by means of probability model checker PRISM. In addition, multi-directional probability and expected reward evaluation analyses are carried out from the point of view of time. The simulation results show that, with the failure of multiple V2I links, the network quality of service (QoS) correspondingly declines, but the network still survives, due to the multi-path transmission control protocol (MPTCP) action. Moreover, with a high fault repair rate, the service performance and survivability of the network is improved rapidly.