Gait recognition is an important biometric technique for video surveillance tasks, due to the advantage of using it at distance. In this paper, we present a persistent homology-based method to extract topological features (the so-called {\it topological gait signature}) from the the body silhouettes of a gait sequence. % It has been used before in several conference papers of the same authors for human identification, gender classification, carried object detection and monitoring human activities at distance. % The novelty of this paper is the study of the stability of the topological gait signature under small perturbations and the number of gait cycles contained in a gait sequence. In other words, we show that the topological gait signature is robust to the presence of noise in the body silhouettes and to the number of gait cycles contained in a given gait sequence. % We also show that computing our topological gait signature of only the lowest fourth part of the body silhouette, we avoid the upper body movements that are unrelated to the natural dynamic of the gait, caused for example by carrying a bag or wearing a coat.