Because environmental conditions are rarely stable in nature, populations must constantly adapt to changing environments for their persistence. High standing genetic variation and rapid adaptation, though crucial for evolutionary rescue and population viability, might be difficult to be achieved simultaneously because of life history trade-offs: long-lived species could maintain genetic diversity at the expense of the speed of adaptation due to slow generation turnover, while short-lived species could have inverse characteristics. Assessing population viability along the trade-off is necessary to understand evolutionarily optimal life history. Here, we hypothesized that frequency of environmental changes could determine which life history strategy is viable: frequent environmental changes favor fast adaptation, while sporadic changes favor maintaining genetic diversity. To test this prediction, we applied cyclic environmental changes to two-stage structured populations under a variety of life history parameter settings using matrix population models. As a result, we found that all life histories were apt to persist in stable environments, and that short-lived strategies sometimes showed high viability in frequently fluctuating environments depending on the strength of negative density dependence, partly supporting our hypothesis. The results indicate the need to consider density-dependent processes to understand adaptation dynamics under fluctuating environments.