Dengue virus serotypes 1 to 4 (DENV1–4) and Zika virus (ZIKV) are mosquito-borne flaviviruses that induce both virus-specific and broadly reactive antibodies. A first DENV infection is thought to induce antibodies that wane over 2 years to titers that can subsequently enhance severe dengue disease. Secondary DENV infection with a different serotype is thought to induce stable, cross-serotype protective antibodies. Low dengue disease incidence after the recent Zika pandemic led to the hypothesis that ZIKV infection is also transiently cross protective. We investigated antibody kinetics in 4189 children up to 11 years after one and multiple DENV and ZIKV infections in longitudinal cohorts in Nicaragua. We used a DENV inhibition enzyme-linked immunosorbent assay (iELISA), which measures antibodies associated with protection against dengue and Zika disease and with enhancement of dengue disease severity. Unexpectedly, we found that overall DENV iELISA titers stabilized by 8 months after primary DENV infection to a half-life longer than a human life and waned, although gradually, after secondary DENV infection. Similarly, DENV iELISA titers were stable or rose after primary ZIKV infection but declined in individuals with histories of DENV and ZIKV infection. In contrast, kinetics of anti-ZIKV antibodies after ZIKV infection were similar regardless of prior DENV immunity. We observed heterogeneity in DENV iELISA titer, suggesting that individual antibody titer set point, rather than waning, is important for future dengue disease risk. Together, these findings change our understanding of anti-flavivirus antibody kinetics and have implications for measuring vaccine efficacy and for predicting future dengue and Zika outbreaks.