Binge eating is a persistent behavior associated with a chronic course of illness and poor treatment outcomes. While clinical research is unable to capture the full course of binge eating, preclinical approaches offer the opportunity to examine binge-like eating from onset through chronic durations, allowing identification of factors contributing to binge eating persistence. The present study quantified the trajectories of binge-like eating onset and modeled cycles of abstinence/relapse to develop a translational model for binge eating persistence. Adult male and female C57Bl6/J mice were randomized to a binge-like palatable food access schedule (daily 2-hr, 3×/week) or continuous, nonbinge like palatable food access for 12 days (Experiment 1). Persistence of palatable food consumption in both binge-like palatable food access groups was then examined across three cycles of forced abstinence and reexposure to palatable food (incubation) to model the persistence of binge eating in clinical populations. Mice with daily 2-hr palatable food access escalated their intake more than mice in the 3×/week or continuous groups (Experiment 1). This pattern was more pronounced in females. In addition, this pattern of palatable food intake reemerged across multiple cycles of behavioral incubation (Experiment 2). These findings provide a model of binge-like eating in mice that can be used in future studies examining both environmental factors and neural mechanisms contributing to binge eating persistence.