Analyses of an integrated form $N( au)={int}_{ au}^{infty}n( au)d{ au}$ of the distribution of cluster ages, rather than its differential form $n( au)$, demonstrate that the observed distribution has clusters older than about 500 million years in a significant excess over theoretical model distributions. Considerations on cluster disruption processes show that a single disruption time-scale, frequently employed by current theoretical models, is no longer an adequate parameter for describing survival probability of clusters over wide age range, because different initial conditions of these clusters produce corresponding spreads in their lifetimes. To take into account for the spread in initial conditions, we have introduced an age-dependent disruption time, and deduced its age-dependence from the present-day age distribution of clusters. Results show a distinct two-stage variation: The newly introduced disruption time stays constant at about 50 million years for clusters younger than about 100 million years, while for clusters older than that it increases monotonically with the cluster age. This leads us to conclude that clusters experience different types of disrupting causes as they get old.