Studies found that students from low socioeconomic backgrounds have higher odds of dropping out from higher education. Academic hardships were also identified as predictors. The current study utilizes data on 45,752 students who started their studies at The Hebrew University of Jerusalem (2003-2015). Descriptive statistics reveal that 18% of all students dropped out, but that this group is heterogeneous. Specifically, 42% of the dropouts left following academic failures. However, 58% of the dropouts took an existential leave -- never failing a course though taking a limited number of course credits. To identify possible predictors of those dropouts we employ three advanced models: logistic regressions, neural network models and decision tree models. The three methods converge in predicting dropouts when they fail their courses, take a partial programme, or have extremely low GPAs. However, the models fail in predicting the 'existential dropouts' -- the students who never failed, had ostensibly 'ok' grades, and yet decided to leave. The findings set clear criteria for predicting dropout trajectories of academically failing students. We conclude by discussing policy implications that emanate from those new findings and point to the lingering riddle -- and the challenge -- that existential dropouts constitute.