The long-term stability of single-atom catalysts is a major factor affecting their large-scale commercial application. How to evaluate the dynamic stability of single-atom catalysts under working conditions is still lacking. Here, taking a single copper atom embedded in N-doped graphene as an example, the "constant-potential hybrid-solvation dynamic model" is used to evaluate the reversible transformation between copper single atoms and clusters under realistic reaction conditions. It is revealed that the adsorption of H is a vital driving force for the leaching of the Cu single atom from the catalyst surface. The more negative the electrode potential, the stronger the adsorption of H. As a result, the competitive hydrogen evolution reaction is inhibited, and Cu-N bonds are weakened, resulting in some Cu atoms being tethered on the catalyst surface and some being dissolved in the aqueous solution. The collision of the Cu atoms in the two states forms a transient Cu cluster structure as a true catalytic active site to promote CO2 reduction to ethanol. As the applied potential is released or switched to a positive value, hydroxyl radicals (OH•) play a dominant role in the oxidation process of the Cu cluster, and then Cu returns to the initial atomic dispersion state by redeposition, completing the reconstruction cycle of the copper catalyst. Our work provides a fundamental understanding of the dynamic stability of Cu single-atom catalysts under working conditions at the atomic level and calls for a reassessment of the stability of currently reported single-atom catalysts considering realistic reaction conditions.