Cellular vehicle-to-everything (C-V2X) networks provide a promising solution to improve road safety and traffic efficiency. One key challenge in such systems lies in meeting quality-of-service (QoS) requirements of vehicular communication links given limited network resources, particularly under imperfect channel state information (CSI) conditions caused by the highly dynamic environment. In this paper, a novel two-phase framework is proposed to instill resilience into C-V2X networks under unknown imperfect CSI. The resilience of the C-V2X network is defined, quantified, and optimized the first time through two principal dimensions: absorption phase and adaptation phase. Specifically, the probability distribution function (PDF) of the imperfect CSI is estimated during the absorption phase through dedicated absorption power scheme and resource block (RB) assignment. The estimated PDF is further used to analyze the interplay and reveal the tradeoff between these two phases. Then, a novel metric named hazard rate (HR) is exploited to balance the C-V2X network's prioritization on absorption and adaptation. Finally, the estimated PDF is exploited in the adaptation phase to recover the network's QoS through a real-time power allocation optimization. Simulation results demonstrate the superior capability of the proposed framework in sustaining the QoS of the C-V2X network under imperfect CSI. Specifically, in the adaptation phase, the proposed design reduces the vehicle-tovehicle (V2V) delay that exceeds QoS requirement by 35% and 56%, and improves the average vehicle-to-infrastructure (V2I) throughput by 14% and 16% compared to the model-based and data-driven benchmarks, respectively, without compromising the network's QoS in the absorption phase.