Over the past decades, fault diagnosis of discrete event systems has many applications and attracts much attention from researchers and practitioners. With the increasingly high requirements on the reliability of cyber-physical systems such as automated manufacturing systems, fault detection technology has been unprecedentedly developed. Traditional approaches to diagnosability analysis of discrete event systems assume that all the communications between sensors and diagnosers work normally and correctly. However, communication failures may occur anytime, which may cause the loss of observations. This observation loss makes traditional diagnosers fail or report incorrect information. The problem of fault diagnosis against intermittent loss of observations is addressed, i.e., robust diagnosability. In this paper, an approach to robust diagnosability analysis based on labeled Petri nets is presented. A necessary and sufficient condition for robust diagnosability is proposed. We also introduce a verification procedure of robust diagnosability using robust reachability diagnosers.