A fundamental issue arising in mobile ad hoc networks (MANETs) is the selection of the optimal path between any two nodes. A method that has been advocated to improve routing efficiency is to select the most stable path so as to reduce the latency and the overhead due to route reconstruction. In this work, we study both the availability and the duration probability of a routing path that is subject to link failures caused by node mobility. In particular, we focus on the case where the network nodes move according to the Random Direction model, and we derive both exact and approximate (but simple) expressions of these probabilities. Through our results, we study the problem of selecting an optimal route in terms of path availability. Finally, we propose an approach to improve the efficiency of reactive Routing protocols.