Single-atom catalysts (SACs) have exhibited exceptional atomic efficiency and catalytic performance in various reactions but suffer poor stability. Understanding the structure-stability relation is the prerequisite for stability optimization but has been rarely explored due to complexity of the degradation process and reaction environments. Herein, we successfully established the structure-stability relation of N-doped carbon-supports SACs (MN4 SACs) under working conditions of CO2 reduction, by using advanced constant-potential density functional theory calculations. Systematic mechanism investigation that considered different factors identifies the key role of initial hydrogen adsorption on the coordination N atom in catalytic stability, where the feasibility of the adsorption eventually determines the leaching of the metal atom. On this basis, a simple descriptor consisting of electron number and electronegativity is constructed, realizing accurate and rapid prediction of the stability of SACs. Furthermore, strategies via modifying the local geometric structure to improve the stability without changing the active centers are proposed accordingly, which are supported by related experiments. These findings fill the current void in understanding SAC stability under practical working conditions, potentially advancing the widespread application of SACs in sustainable energy conversion systems.