Interactive Digital Storytelling (IDS) enables users to influence the unfolding of a story at the plot level using Artificial Intelligence techniques for generating and balancing narrative paths on the fly. Despite their promise, most IDS systems are still unable to consistently deliver engaging user experiences. To further understand the characteristics of this new media, particularly user engagement, we apply the concept of Continuation Desire to an existing Interactive Narrative to dynamically sample engagement during a play session. We use a comparative study to assess the effects of interrupting users during gameplay. This study found no evidence that, if done properly, interrupting the experience spoils it. We find no significant impact on the desire to play again as a result of introducing interruptions either.