  The persistence probability, $P_C(t)$, of a cluster to remain unaggregated is
studied in cluster-cluster aggregation, when the diffusion coefficient of a
cluster depends on its size $s$ as $D(s) \sim s^\gamma$. In the mean-field the
problem maps to the survival of three annihilating random walkers with
time-dependent noise correlations. For $\gamma \ge 0$ the motion of persistent
clusters becomes asymptotically irrelevant and the mean-field theory provides a
correct description. For $\gamma < 0$ the spatial fluctuations remain relevant
and the persistence probability is overestimated by the random walk theory. The
decay of persistence determines the small size tail of the cluster size
distribution. For $0 < \gamma < 2$ the distribution is flat and, surprisingly,
independent of $\gamma$.
