Dengue is a vector-borne virus that infects humans. In many regions there are seasonal oscillations in the mosquito population size. Consequently dengue transmission and incidence may become very low, or vanish, during cold or dry periods but the virus returns when environmental conditions become favorable again. Laboratory studies indicate that between 0.01% and 10% of the offspring of an infected female mosquito are also infected, and it has been suggested that this vertical transmission may allow the virus to persist from season to season. I will examine the feasibility of this hypothesis using a stochastic SIR type mathematical model considering, in particular, how the efficiency of vertical transmission required to prevent virus extinction depends on the magnitude of seasonal variation in the mosquito population.