The effects of discrete interventions and naturally-occurring events on a person's thoughts, emotions, behaviors, and physical functioning often vary over time. As such, understanding temporal persistence or decay of effects is of central importance in behavioral sciences and it entails recognizing changes after a person has been subject to a treatment, establishing a cause-and-effect and evaluating the persistence of the effect with the passage of time. In this study, we develop an effect persistence model for intensive longitudinal data under a general assumption of an exponential loss of association between exposure and outcome over time. The proposed model may be useful for understanding the complexity of phenomena where subjects can be repeatedly exposed to an intervention while at the same time, the effect of any one exposure is expected to diminish over time. The method is motivated by, and applied to data from a study of adolescent exposure to pro-smoking advertisement where the impact of pro-smoking media exposure on young adults' susceptibility to smoking is assessed along with the decay of the effect over time. The performance of the proposed method is investigated.