Energy conservation is a central issue in the design of a wireless mesh network powered by solar cells. Since traffic uncertainty is always present, in this paper, we study how to design an energy-conservation routing scheme in face of traffic uncertainty. We present a new approach that is immune from the two problems prevalent in conventional approaches: performance degradation caused by inaccuracy of a simplified interference model and the instability caused by the assumption of unbounded transmission power and data rate. The analytical and simulation results presented in this paper show that the proposed approach can achieve significant performance gains, in terms of throughput and energy consumption, over the conventional approach.