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Sensor-based sleep monitoring systems can be used to track sleep behavior on a daily basis and provide feedback to their users to promote health and well-being. Such systems can provide data visualizations to enable self-reflection on sleep habits or a sleep coaching service to improve sleep quality. To provide useful feedback, sleep monitoring systems must be able to recognize whether an individual is sleeping or awake. Existing approaches to infer sleep-wake phases, however, typically assume continuous streams of data to be available at inference time. In real-world settings, though, data streams or data samples may be missing, causing severe performance degradation of models trained on complete data streams. In this paper, we investigate the impact of missing data to recognize sleep and wake, and use regression-and interpolation-based imputation strategies to mitigate the errors that might be caused by incomplete data. To evaluate our approach, we use a data set that includes physiological traces-collected using wristbands-, behavioral data-gathered using smartphones-and self-reports from 16 participants over 30 days. Our results show that the presence of missing sensor data degrades the balanced accuracy of the classifier on average by 10-35 percentage points for detecting sleep and wake depending on the missing data rate. The impu-tation strategies explored in this work increase the performance of the classifier by 4-30 percentage points. These results open up new opportunities to improve the robustness of sleep monitoring systems against missing data.