Vesicular stomatitis virus has the potential for very rapid evolution in the laboratory, but like many other arboviruses, it evolves at a relatively slow rate in the natural environment. Previous work showed that alternating replication in different cell types does not promote stasis. In order to determine whether other factors promote stasis, we compared the fitness trajectories of populations evolving during acute infections in mammalian cells, populations evolving during persistent infections in insect cells, and populations evolving during alternating acute and persistent infection cycles. Populations evolving under constant conditions increased in fitness in the environment in which they replicated. An asymmetric trade-off was observed such that acute infection had no cost for persistence but persistent replication had a dramatic cost for acute infection in mammalian cells. After an initial period of increase, fitness remained approximately constant in all the populations that included persistent replication, but fitness continuously increased in populations evolving during acute infections. Determination of the consensus sequence of the genes encoding the N, P, M, and G proteins showed that the pattern of mutation accumulation was coherent with fitness changes during persistence so that once fitness reached a maximum, the rate of mutation accumulation dropped. Persistent replication dominated both the genetic and the phenotypic evolution of the populations that alternated between acute infection of mammalian cells and persistence in insect cells, and fitness loss was observed in the mammalian environment despite periodic replication in mammalian cells. These results show that stasis can be achieved without good levels of adaptation to both the mammalian and the insect environments.