We perform a theoretical study of the nonlinear dynamics of nonlinear optical isolator devices based on coupled microcavities with gain and loss. This reveals a correspondence between the boundary of asymptotic stability in the nonlinear regime, where gain saturation is present, and the PT -breaking transition in the underlying linear system. For zero detuning and weak input intensity, the onset of optical isolation can be rigorously derived, and corresponds precisely to the transition into the PT -broken phase of the linear system. When the couplings to the external ports are unequal, the isolation ratio exhibits an abrupt jump at the transition point, whose magnitude is given by the ratio of the couplings. This phenomenon could be exploited to realize an actively controlled nonlinear optical isolator, in which strong optical isolation can be turned on and off by tiny variations in the inter-resonator separation.