Fundamental requirements of millimeter wave (mmWave) systems are peak data rates of multiple Gbps and latencies of the order of at most a few milliseconds. However, highly directional mmWave links are susceptible to frequent link failures under stress conditions such as mobility and human blockage. Under these conditions, multi-hop routing can achieve reliable and robust performance. In this paper, we consider multi-hop mmWave systems and propose proactive route refinement schemes under dynamic scenarios. First, we consider the AODV-type protocols and propose a cross-layer approach that integrates sectorized communication at the MAC layer with on-demand multi-hop routing at the network layer. Next, we consider Backpressure routing protocol, and enhance this protocol with periodic HELLO status messages. System-level simulation results based on the IEEE 802.11ad standard confirm the benefits of proactive route refinement for the ADOV-type and Backpressure routing protocols.