Achieving and maintaining user engagement is a key goal of human-robot interaction. This paper presents a method for determining user engagement state from physiological data (including galvanic skin response and skin temperature). In the reported study, physiological data were measured while participants played a wire puzzle game moderated by either a simulated or embodied robot, both with varying personalities. The resulting physiological data were segmented and classified based both on position within trial and trial number using the K-Nearest Neighbors algorithm. We found it was possible to estimate the user's likelihood of quitting a trial for trials of variable length with an accuracy of 83.87%. In future experiments, this ability would allow assistive robot moderators to determine the user's likelihood of ending an interaction at any given point during the interaction. This knowledge could then be used to adapt the behavior of the robot in an attempt to re-engage the user.