Intelligent reflecting surfaces (IRSs) are envisioned as a transformative method for enhancing the physical layer security of future communication networks. However, current IRS-assisted secure wireless system designs incur high time cost for the joint optimization of beamforming vectors and IRS phase shifts and are susceptible to unforeseen disruption. Therefore, introducing resilience in IRS-assisted secure systems is essential. In this paper, we first quantify the resilience performance as the combination of the absorption and adaptation performance. In particular, the absorption performance measures the system's robustness when facing failure while the adaptation performance reflects the system's ability to recover from failure. Then, we propose a two-timescale transmission protocol aiming to enhance system resilience while limiting maximum information leakage to eavesdroppers. Specifically, in the initialization phase, the base station (BS) beamforming vectors and IRS phase shifts are optimized iteratively using an alternating optimization (AO) approach to improve the absorption performance of the system, i.e., the worst-case achievable rate, given a predefined maximum tolerable leakage rate, by accounting for the impact of long-term channel variations. When the system detects an outage, a fast system recovery mechanism is activated to restore operation by adjusting only the BS beamforming vectors, which enhances the adaptation performance of the system. Our numerical results reveal that the proposed algorithm significantly improves system resilience, including system robustness and recovery performance. Moreover, the proposed design guarantees outage-free transmission over a long time interval for moderate-size IRSs.