A central goal of many marine protected areas is ensuring the persistence of fish populations, which depends on the life history characteristics and movement patterns of individual species. While previous studies have focused on species where adults are sedentary, the current study examines an age-structured diffusion model for a one-species system in a single spatial dimension. We define persistence as a positive growth rate for small populations and determine conditions that will yield a positive growth rate. We find that the minimum fraction of habitat needed to be off-limits to fishing depends on two dimensionless parameters representing the net birth rate in the reserve, measured in the time it takes to move the length of the habitat, and the net death rate in the fished area, in that same time. Of the two parameters, natural population growth rate has a larger impact on reserve size than the net death rate due to fishing, although their ratio is useful for determining reserve size. These results suggest that reserves are appropriate for mobile species having at least one of several qualities: (1) small movement rates, (2) high birth rates relative to fishing rates or (3) large habitat sizes.