Memristive spiking neural network (SNN) chips with high energy efficiency, high speed, and high integration density are highly promising for space information processing system applications. The memristive neuron circuit is a core component in memristive SNN hardware. Within these circuits, threshold switching memristors (TSMs) are fundamental to realizing spiking behavior. Experiments have shown that TSM devices are susceptible to various types of radiation in space environments, which can disrupt the spiking characteristics of neural circuits and degrade the performance of SNN chips. Therefore, it is particularly important to implement radiation-hardening design for memristive SNN chips. However, the current absence of TSM radiation damage models presents a major challenge for the radiation-hardening design of memristive neuron circuits and memristive SNN chips. In this work, we developed a compact damage model based on the experimental data of atmospheric neutron irradiated Au/Ag:Ta₂O₅/Pt threshold switching memristors. Using this model, we simulated the I-V characteristics of the threshold switching memristors to compare their performance before and after irradiation. The simulation results are in strong agreement with the experimental data, as evidenced by coefficients of determination (R²) consistently exceeding 0.89 (specifically 0.8911, 0.89621, 0.95756, and 0.96305). Subsequently, this validated model was employed to guide the radiation-hardening optimization of the memristive Leaky Integrate-and-Fire (LIF) neuron circuit. The memristive LIF neuron circuit reveals significant differences between its unoptimized and optimized versions in simulations. Specifically, for the unoptimized circuit, the spike firing frequency decreases dramatically after irradiation, dropping from 23.3 kHz to 11.6 kHz. In stark contrast, the spike firing frequency of the optimized circuit exhibits only a slight decrease after irradiation, dropping from 25 kHz to 23.3 kHz, indicating its excellent radiation tolerance. When this optimized circuit was applied to an SNN, the results indicate that its final recognition accuracy after irradiation reaches 97.2%, significantly higher than the 94.7% under the unoptimized design. This work lays the groundwork for the design of memristive SNN chips in neutron radiation environments.