Previous face traversal algorithms for ad-hoc routing all assume static graphs during the routing process. In this paper, we present a new face traversal algorithm that does not rely on this assumption. Specifically, we consider routing on edge dynamic graphs, which have stationary nodes and whose edges may change between being active and inactive at any time. The algorithm guarantees message delivery if there exists a sequence of connected spanning subgraphs of the routing graph, each of which is stable for a sufficiently long period of time. Moreover, the algorithm tolerates a wide array of transient faults.