Most research in fault diagnosis of discrete event systems has been focused on permanent failures. However, experience with monitoring of dynamic systems shows that intermittent faults are predominant, and that their diagnosis constitutes one of the most challenging tasks for surveillance activities. Among the main existing approaches to deal with permanent faults, two were widely investigated while considering different settings: the Diagnoser based approach, and the Twin-plant based approach. The latter was developed to cope with some complexity limitations of the former. In the present paper, we propose a twin-plant based approach to deal with diagnosability of intermittent faults. Firstly, we discuss various notions of diagnosability, while considering the occurrence of faults, their recovery, and the identification of the system status. Then, we establish the necessary and sufficient conditions for each notion, and develop on-the-fly algorithms to check these properties. The discussed approach is implemented in a prototype tool that is used to conduct experiments on a railway control benchmark.