In this study, the robust detection problem of intermittent faults (IFs) for linear stochastic systems subject to time-varying parametric perturbations is addressed. The authors consider the case that an IF appears and disappears non-deterministically, and lasts for random periods of active time with unknown magnitudes. A novel robust fault detection method is presented to detect all the appearing time and the disappearing time of an IF. Based on the output of an observer-type residual generator, a novel robust residual is constructed by utilising a sliding-time window. Two hypothesis tests are provided to detect all the appearing and the disappearing time, respectively. Moreover, the detectability of the IF by using the proposed robust detection scheme is defined in a probabilistic sense, and a sufficient detectability condition is presented within the given framework. Capacities of false alarm rates and missed detection rates are rigorously analysed. Finally, the application of the presented scheme is illustrated on a simplified radial flight control system and the results show that the IF can be effectively detected in the presence of perturbations and noises.