Summary 1.The arctic fox Vulpes lagopus in Fennoscandia was heavily decimated in the early 20th century and has failed to recover despite full protection during the last 70 years. On the contrary, since the 1970s the population has declined even further and the species is now on the verge of regional extinction. 2.The most recent population decline of the arctic fox in Fennoscandia has coincided with some distinct changes in the cyclic population dynamics of its key prey, lemmings and voles. Although this coincidence of events and the tight trophic connection between foxes and rodents suggest that the two phenomena are causally linked, the effects of spatio-temporal small rodent dynamics on the viability of arctic fox populations have not been fully explored. 3. Here we address how the mean, temporal variance and the periodicity of small rodent population density cycles impact long-term stochastic growth rate of arctic fox populations. We do this in a modelling framework where the vital rates of the fox are linked to realistic, quantitative realizations of small rodent density dynamics. 4. Arctic fox population growth rate was found to be highly sensitive to the temporal mean and to some extent to the variance in small rodent density cycles, whereas cycle period in the observed range of 3-to 5-year cycles was surprisingly of minor importance. 5. Synthesis and applications . Our analysis shows that small rodent population dynamics characterized by low-amplitude density cycles (irrespective of their average cycle period), provide little scope for positive population growth, and thus recovery, of the arctic fox. Thus, we advise that management actions such as re-introductions and red fox Vulpes vulpes control should be conducted in mountain tundra regions where regular, high-amplitude cycles, of any period, with recurrent high spring densities of rodents still prevail. In order to properly identify geographic areas with the highest potential for arctic fox recovery, the emphasis of current monitoring programmes of small rodent dynamics needs to consider more quantitative metrics than they currently employ.