<p>In data-driven optimization, the true probability distribution of the random variable is often estimated from empirical data which may be unreliable. To mitigate the resulting uncertainty, the robust satisficing model is proposed in the literature to allow for a trade-off between target violations and improved robustness. This paper primarily focuses on stability analysis of the robust satisficing model under the Wasserstein distance and the Kullback–Leibler divergence, including continuity of the optimal value, the set of optimal solutions, and the deviation between the expected cost and target, and the quantitative statistical robustness of the optimal value function. These results demonstrate that, under certain conditions, the overshoot of the expected cost under the true probability distribution above the target is continuous with respect to the perturbation of the reference probability distribution and the optimal values remain stable with respect to small perturbations in the observed data, thereby ensuring reliable performance even in the presence of noisy samples.</p>