Networked control has been used more and more widely in engineering systems. To study networked control for discrete event systems, network controllability and network observability are introduced in our previous work on networked supervisory control theory. In this paper, we investigate robust supervisory control for networked discrete event systems. We assume that the system to be controlled is not known precisely. We only know that it is one among several possibilities. The goal is to design a robust supervisor that works for all possibilities. We derive a necessary and sufficient condition for the existence of such a robust supervisor. The condition must take into account the communication delays and losses in both observation channel and control channel. We show that the existence condition is characterized by network controllability and network observability that are keys to control networked discrete event systems.