  Active fluids such as bacterial swarms, self-propelled colloids, and cell
tissues can all display complex spatio-temporal vortices that are reminiscent
of inertial turbulence. This emergent behavior despite the overdamped nature of
these systems is the hallmark of active turbulence. In this letter, using a
generalized hydrodynamic model, we present a study of the persistence problem
in active turbulence. We report that the persistence time of passive tracers
inside the coherent vortices follows a Weibull probability density whose shape
and scale are decided by the strength of activity -- contrary to inertial
turbulence that displays power-law statistics in this region. In the turbulent
background, the persistence time is exponentially distributed that is remindful
of inertial turbulence. Finally we show that the driver of persistence inside
the coherent vortices is the temporal decorrelation of the topological field,
whereas it is the vortex turnover time in the turbulent background.
