Thin tropical cirrus clouds influence the radiative and stratospheric water vapor budgets, yet the processes controlling their persistence remain poorly constrained. Here, we investigate the impact of multiscale wave-driven vertical wind speed and temperature fluctuations on thin tropical cirrus lifetime using a Lagrangian microphysical model initialized from lidar observations obtained during the Strateole-2 campaigns. The model represents the evolution of ice crystal populations under stochastic high-frequency gravity wave forcing and an idealized low-frequency inertia gravity wave. Our results show that cirrus lifetime is controlled by a competition between stabilization through multiscale cooling fluctuations and complete sublimation by rare, high amplitude warming events due to gravity waves. This introduces a threshold behavior: if some ice crystals can grow large enough without being dissipated in the first hours of the lifetime, they become less sensitive to complete sublimation and enter a stabilization regime in which sedimentation determines the cloud lifetime. Stronger gravity-wave activity shifts this stabilization regime toward larger crystal sizes and generally shortens cirrus lifetime. Lower frequency waves modulate this evolution by setting the slowly varying background temperature. Cooling phases promote crystal growth and favor long-lived cirrus, while warming phases enhance rapid cloud decay. The simulated lifetime distribution reproduces the strongly skewed distribution of observed thin tropical cirrus lifetimes, including a non negligible population of clouds which persists longer than 12 h, and dominates the total cloud coverage.