Humanoid robots are promising approach to automating patient interviews routinely conducted by medical staff. Their human-like appearance enables them to use the full gamut of verbal and behavioral cues that are critical to a successful interview. On the other hand, anthropomorphism can induce expectations of human-level performance by the robot. Not meeting such expectations degrades the quality of interaction. Specifically, humans expect rich real-time interactions during speech exchange, such as backchanneling and barge-ins. The nature of the patient interview task differs from most other scenarios where task oriented dialogue systems have been used, as there is increased potential of engagement breakdown during interaction. We describe a dialogue system architecture that improves the performance of humanoid robots on the patient interview task. Our architecture adds a nested inner real-time control loop to improve the timeliness of the robot's responses based on the notion of "stance", an elaboration of the concept of a "turn", common in most existing dialogue systems. It also expands the dialogue state to monitor not only task progress, but also human engagement. Experiments using a humanoid robot running our proposed architecture reveal improved performance on interview tasks in terms of the perceived timeliness of responses and users' impressions of the system. © 2024 IEEE.