The article explores robust estimators in logistic regression models, focusing on their breakdown points. While previous research has proposed various estimators, their breakdown points were often unknown. The study found that in logistic regression models with binary data, no estimator has a high finite sample breakdown point under a weak condition. However, modifications of certain estimators have breakdown points of approximately 1/2 in models with large strata. These estimators are consistent in a large supermodel of the logistic regression model, and existing programs can be used to compute them.