RNA viruses display high mutation rates and their populations replicate as dynamic and complex mutant distributions, termed viral quasispecies. Repeated genetic bottlenecks, which experimentally are carried out through serial plaque-to-plaque transfers of the virus, lead to fitness decrease (measured here as diminished capacity to produce infectious progeny). Here we report an analysis of fitness evolution of several low fitness foot-and-mouth disease virus clones subjected to 50 plaque-to-plaque transfers. Unexpectedly, fitness decrease, rather than being continuous and monotonic, displayed a fluctuating pattern, which was influenced by both the virus and the state of the host cell as shown by effects of recent cell passage history. The amplitude of the fluctuations increased as fitness decreased, resulting in a remarkable resistance of virus to extinction. Whereas the frequency distribution of fitness in control (independent) experiments follows a log-normal distribution, the probability of fitness values in the evolving bottlenecked populations fitted a Weibull distribution. We suggest that multiple functions of viral genomic RNA and its encoded proteins, subjected to high mutational pressure, interact with cellular components to produce this nontrivial, fluctuating pattern.