An apparatus, program product and method utilize on-demand propagation of routing information to reduce the overhead associated with distributing routing information throughout a distributed computing system. The staleness of the routing information utilized in routing client requests for a particular client is gauged based upon the number and/or frequency of client requests issued for that client that require rerouting, e.g., as indicated in responses returned in response to the client requests. Once the reroutes of client requests meet a desired propagation criterion, updated routing information is then requested for the client.