Facultative sex combines sexual and asexual reproduction in the same individual (or clone) and allows for a large diversity of life-history patterns regarding the timing, frequency and intensity of sexual episodes. In addition, other life-history traits such as a diapause stage may become linked to sex. Here, we develop a matrix modelling framework for addressing the cost of sex in facultative sexuals, in constant, periodic and stochastically fluctuating environments. The model is parametrized using life-history data from Brachionus calyciflorus, a facultative sexual rotifer in which sex and diapause are linked. Sexual propensity was an important driver of costs in constant environments, in which high costs (always > onefold, and sometimes > twofold) indicated that asexuals should outcompete facultative sexuals. By contrast, stochastic environments with high temporal autocorrelation favoured facultative sex over obligate asex, in particular, if the penalty to fecundity in 'bad' environments was large. In such environments, obligate asexuals were constrained by their life cycle length (i.e. time from birth to last reproductive adult age class), which determined an upper limit to the number of consecutive bad periods they could tolerate. Nevertheless, when facultative asexuals with different sexual propensities competed simultaneously against each other and asex, the lowest sex propensity was the most successful in stochastic environments with positive autocorrelation. Our results suggest that a highly specific mechanism (i.e. diapause linked to sex) can alone stabilize facultative sex in these animals, and protect it from invasion of both asexual and pure sexual strategies.This article is part of the themed issue 'Weird sex: the underappreciated diversity of sexual reproduction'.