We present a game-theoretic framework for modeling and solving routing problems in dynamically changing networks. The model covers the aspects of reactivity and non-termination, and it is motivated by quality-of-service provisioning in cognitive radio networks where data transmissions are interfered by primary systems. More precisely, we propose an infinite two-player game where a routing agent has to deliver network packets to their destinations while an adversary produces demands by generating packets and blocking connections. We obtain results on the status of basic problems, by showing principal limitations to solvability of routing requirements and singling out cases with algorithmic solutions.