In this paper, an approach to analyze diagnosability of intermittent failures in discrete-event systems (DESs) is developed. The analysis is performed based on the twin-plant structure generated from the input model, which is a finite state automaton (FSA), where states are partitioned according to the predefined failure conditions of the system. Two definitions of diagnosability, regarding the occurrence of failures and their normalization (i.e., the disappearance of failures) are discussed. Necessary and sufficient conditions for diagnosability are developed and proved. Then, an incremental algorithm to actually check such conditions is elaborated. Finally, a benchmark is given to both illustrate the various concepts discussed and assess the efficiency of the proposed approach.