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Globally, millions of women track their menstrual cycle and fertility via smartphone-based health apps, generating multivariate time series with frequent missing data. To leverage this type of data for studies of fertility or studies of the effect of the menstrual cycle on symptoms and diseases, it is critical to have methods for identifying reproductive events, such as ovulation, pregnancy losses or births. Here, we present a hierarchical approach relying on hidden semi-Markov models that adapts to changes in tracking behavior, explicitly captures variable- and state- dependent missingness, allows for variables of different type, and quantifies uncertainty. The accuracy on simulated data reaches 98% with no missing data and 90% with realistic missingness. On our partially labeled real-world time series, the accuracy reaches 93%. Our method also accurately predicts cycle length by learning user characteristics. Its implementation is publicly available (HiddenSemiMarkov R package) and transferable to any health time series, including self-reported symptoms and occasional tests.