Executive dysfunction is a deficiency in skills of planning and problem solving that characterizes many neuropsychiatric disorders. The Towers Task is a commonly used measure of planning and problem solving for assessing executive function. Towers Task data are usually zero-inflated and right-censored, and ignoring these features can result in biased inference for the disease characterization of executive dysfunction. In this manuscript, a mixed-effects model for longitudinal censored semicontinuous data is developed for analyzing longitudinal Towers Task data from the PREDICT-HD study. The model is contrasted with current practice, and implications for general use are discussed.