Reproduction is a fundamental biological process, with organisms reproducing sexually, asexually, and, in some cases, utilizing both modes of reproduction within the same population. Does the ability to reproduce through a combination of asexual and sexual modes offer an evolutionary advantage over relying on either mode alone? Here, we introduce an empirically driven theoretical model to examine the dynamics and interplay between sexual and asexual reproduction in stick insect populations. We analyse it using a novel phase transition approach and corroborate it using published experimental data. We find that the presence of males can either increase or decrease the overall population size. However, maintaining an optimal ratio of parthenogenetic to sexual reproduction is crucial for male resilience, effectively delaying male extinction. Conversely, extreme levels of parthenogenetic reproduction-whether too high or too low-can lead to male extinction, emphasizing the need for a balanced number of virgin females to ensure the persistence of males. Our model also explains male absence in Carausius morosus and persistence in Extatosoma tiaratum. Our findings provide valuable insights into the interplay of reproductive strategies and contribute to broader discussions on the transitions between sexual and asexual reproduction.