Heterogeneity is omnipresent in living systems and biophysical diversity enriches the systems’ dynamical repertoire. However, it remains challenging to reconcile with the robustness and persistence of the systems functions over time, which is called resilience. To better understand the underlying mechanism of resilience, we considered a nonlinear neural network model focussing on the relationship between excitability heterogeneity of neurons and resilience. To quantify the degree of resilience, we considered the number of stationary states present in the system and how they are affected by parameters. This impact on the number of stationary states is known as trivialization. We analyzed both analytically and numerically gradient and non-gradient systems modeled as non-linear sparse neural networks evolving over long time scales. Excitability heterogeneity in neurons tuned network stability in a context-dependent way, quenched the number of stationary states and enhanced resilience. This heterogeneity was found to implement a homeostatic control mechanism enhancing network resilience to changes in network size and connection probability by quenching the system’s dynamic volatility.