  In this paper we explore the evolution of transport capacity on networks with
stochastic incidence of damage and accumulation of faults in their connections.
For each damaged configuration of the network, we analyze a Markovian random
walker that hops over weighted links that quantify the capacity of transport of
each connection. The weights of the links in the network evolve due to randomly
occurring damage effects that reduce gradually the transport capacity of the
structure. We introduce a global measure to determine the functionality of each
configuration and how the system ages due to the accumulation of damage that
cannot be repaired completely. Then, by assuming a minimum value of the
functionality required for the system to be "alive", we explore the statistics
of the lifetimes for several realizations of this process in different types of
networks. Finally, we analyze the characteristic longevity of such a system and
its relation with the "complexity" of the network structure. One finding is
that systems with greater complexity live longer. Our approach introduces a
model of aging processes relating the reduction of functionality with the
accumulation of "misrepairs" and the lifetime of a complex system.
