Prevailing models typically treat cognitive aging as gradual, with rates of change evolving slowly over time and individual differences expressed mainly as variation in level, onset, and rate of decline. We test this view against an alternative in which individual trajectories are organised as extended plateaus of stability punctuated by brief episodes of accelerated loss. Harmonising 728,000 memory tests from 80,000 participants across three population cohorts, we introduce a simulation-calibrated framework to identify genuine memory stability. 10% of adults ≥ 70 showed stable performance over a decade, and in an MRI subgroup (n ≈ 2,000), these individuals exhibited lower rates of brain atrophy, linking cognitive stability to brain maintenance. However, analyses projecting trajectories backward in time showed that many late-life stable trajectories would imply implausibly low mid-life performance, indicating prior unobserved decline. Across individuals, 54% showed at least one stability period lasting 10 years, but only 0.4% maintained stability over 24 years under our criterion. Models based solely on gradual decline are insufficient to account for the observed temporal structure of memory change, and smooth population-level decline can emerge from punctuated individual dynamics. Together, the findings align with a complex-systems view where stability is often a transient state rather than a lifelong trait.