Seasonally dry ecosystems exhibit periods of high water availability followed by extended intervals during which rainfall is negligible and streamflows decline. Eventually, such declining flows will fall below the minimum values required to support ecosystem functions or services. The time at which dry season flows drop below these minimum values (Q*), relative to the start of the dry season, is termed the "persistence time'' (T-Q*). The persistence time determines how long seasonal streams can support various human or ecological functions during the dry season. In this study, we extended recent work in the stochastic hydrology of seasonally dry climates to develop an analytical model for the probability distribution function (PDF) of the persistence time. The proposed model accurately captures the mean of the persistence time distribution, but underestimates its variance. We demonstrate that this underestimation arises in part due to correlation between the parameters used to describe the dry season recession, but that this correlation can be removed by rescaling the flow variables. The mean persistence time predictions form one example of the broader class of streamflow statistics known as crossing properties, which could feasibly be combined with simple ecological models to form a basis for rapid risk assessment under different climate or management scenarios.