Wild turkeys (Meleagris gallopavo) are a prolific species and valuable game animal throughout the United States. Stochastic simulations are commonly used to inform harvest management, and we used simulation to test performance of fall harvest management that included 1‐, 3‐, and 5‐year cycles of population assessment and updating of harvest targets, respectively. To assess robustness of our conclusions, we replicated analyses across 18 combinations of model parameters that included population productivity (3 levels), sex‐specific vulnerability to fall harvest (3 levels), and magnitude of spring harvest (2 levels). Performance of multi‐year cycles, measured using abundance of males and annual harvest, depended on the context of model parameters that interacted to determine responses of populations to harvest. One‐ and 3‐year cycles had similar performance so long as female harvests were less than or equal to male harvests. However, when harvest of females was greater than males, or when 5‐year regulation cycles were implemented, there was greater risk due to nonlinear population responses to increased harvest. For example, nonlinearity resulted in thresholds where declines to abundance and harvest could occur with small increases to harvest rates, and thus the sustainability of fall harvests was less robust for multi‐year cycles with time‐lagged assessment and decision making. Moreover, the harvest rate resulting in threshold responses depended on model parameters and often occurred within the range of harvest rates recommended by earlier modeling studies (7–15%). Our results imply that multi‐year cycles can be a viable approach to harvest management. Monitoring that provides information on sex‐specific harvest is recommended, however, to determine if nonlinear population responses should be anticipated. Ideally, information on population‐specific vital rates would also be available to allow managers to avoid harvest rates near thresholds that are expected to result in population declines. © The Wildlife Society, 2019