Rift Valley fever (RVF) is an emerging zoonotic mosquito-borne infectious disease that has been identified as a risk for spread to other continents and can cause mass livestock mortality. In equatorial Africa, outbreaks of RVF are associated with high rainfall, when vector populations are at their highest. It is, however, unclear how RVF virus persists during the inter-epidemic periods and between seasons. Understanding inter-epidemic persistence as well as the role of vectors and hosts is paramount to creating effective management programmes for RVF control. We created a mathematical model for the spread of RVF and used the model to explore different scenarios of persistence including vertical transmission and alternate wildlife hosts, with a case study on buffalo in Kruger National Park, South Africa. Our results suggest that RVF persistence is a delicate balance between numerous species of susceptible hosts, mosquito species, vertical transmission and environmental stochasticity. Further investigations should not focus on a single species, but should instead consider a myriad of susceptible host species when seeking to understand disease dynamics.