Organisms must cope with both short- and long-term environmental changes to persist. In this study we investigated whether life histories trade-off between their robustness to short-term environmental perturbations and their ability to evolve directional trait changes. We could confirm the tradeoff by modeling the eco-evolutionary dynamics of life-histories along the fast-slow pace-of-life continuum. Offspring dormancy and high adult survival rates allowed for large population sizes to be maintained in face of interannual environmental fluctuations but limited the speed of trait evolution with ongoing environmental change. In contrast, precocious offspring maturation and short-living adults promoted evolvability while lowering demographic robustness. This tradeoff had immediate consequences on extinction dynamics in variable environments. High evolvability allowed short-lived species to cope with long-lasting gradual environmental change, but came at the expense of more pronounced population declines and extinction rates from environmental variability. Higher robustness of slow life-histories helped them persist better on short timescales.