On-demand routing protocols discover routes only when the source node has a packet to send to the destination. These protocols cache previously discovered routes in order to reduce the routing overheads as well as to decrease the route discovery latency. Mobility of the nodes in ad hoc wireless networks impact the performance of the routing protocols significantly. Mobility alters the validity and lifetime of routes cached by the nodes. However, due to the on-demand nature of the routing protocol, the link status will not get updated until it is used. For example, even if a link is up, some of the routes associated with this link may still be invalid because of other failed links in their paths. In this context, route expiry time plays a critical role in determining the performance of the routing protocol. Inefficient choice of route expiry time results in stale routes or early expired routes which degrade the overall performance of the protocol. The route expiry time should be chosen in such a way that it reduces the control overhead caused by the route discovery process. This paper presents a statistical model for estimating route expiry time adaptively, that results in reduced control traffic in on-demand ad hoc networks