  We study the probability, $P_S(t)$, of a cluster to remain intact in
one-dimensional cluster-cluster aggregation when the cluster diffusion
coefficient scales with size as $D(s) \sim s^\gamma$. $P_S(t)$ exhibits a
stretched exponential decay for $\gamma < 0$ and the power-laws $t^{-3/2}$ for
$\gamma=0$, and $t^{-2/(2-\gamma)}$ for $0<\gamma<2$. A random walk picture
explains the discontinuous and non-monotonic behavior of the exponent. The
decay of $P_S(t)$ determines the polydispersity exponent, $\tau$, which
describes the size distribution for small clusters. Surprisingly,
$\tau(\gamma)$ is a constant $\tau = 0$ for $0<\gamma<2$.
