Feedback dynamic routing is a commonly used control strategy in transportation systems. This class of control strategies rely on real-time information about the traffic state in each link. However, such information may not always be observable due to temporary sensing faults. In this article, we consider dynamic routing over two parallel routes, where the sensing on each link is subject to recurrent and random faults. The faults occur and clear according to a finite-state Markov chain. When the sensing is faulty on a link, the traffic state on that link appears to be zero to the controller. Building on the theories of Markov processes and monotone dynamical systems, we derive lower and upper bounds for the resilience score, i.e. the guaranteed throughput of the network, in the face of sensing faults by establishing stability conditions for the network. We use these results to study how a variety of key parameters affect the resilience score of the network. The main conclusions are: (i) Sensing faults can reduce throughput and destabilize a nominally stable network; (ii) A higher failure rate does not necessarily reduce throughput, and there may exist a worst rate that minimizes throughput; (iii) Higher correlation between the failure probabilities of two links leads to greater throughput; (iv) A large difference in capacity between two links can result in a drop in throughput.