Service discovery architectures and clusterassisted routing protocols in mobile ad-hoc networks (MANETs) heavily use formation and maintenance of a virtual backbone (VB), where the most stable mobile nodes with higher node degree are dynamically selected as the backbone nodes. In this paper we present a novel analytic model for VB stability in MANETs. The model employs the dynamics of node movements, where link creation/failure is modeled via a random walk with probabilistic state-transition matrix. The backbone formation algorithm gives preference to the nodes with the smaller number of link changes and the higher degree. Therefore, the link arrivals and departures determine the probability (and thus the expected time) for a mobile node to leave, join, or remain in the backbone, i.e., the stability of a dynamic structure of VB.