  We study the robustness of an evolving system that is driven by successive
inclusions of new elements or constituents with $m$ random interactions to
older ones. Each constitutive element in the model stays either active or is
temporarily inactivated depending upon the influence of the other active
elements. If the time spent by an element in the inactivated state reaches
$T_W$, it gets extinct. The phase diagram of this dynamic model as a function
of $m$ and $T_W$ is investigated by numerical and analytical methods and as a
result both growing (robust) as well as non-growing (volatile) phases are
identified. It is also found that larger time limit $T_W$ enhances the system's
robustness against the inclusion of new elements, mainly due to the system's
increased ability to reject "falling-together" type attacks. Our results
suggest that the ability of an element to survive in an unfavorable situation
for a while, either as a minority or in a dormant state, could improve the
robustness of the entire system.
