We consider a massless, minimally coupled scalar with a quartic self-interaction which is released in Bunch-Davies vacuum in the locally de Sitter background of an inflating universe. It was shown, in this system, that quantum effects can induce a temporary phase of superacceleration, causing a violation of the weak energy condition on cosmological scales. In this paper, we investigate the system's stability by studying the behavior of linearized perturbations in the quantum-corrected effective field equation at one- and two-loop order. We show that the amplitude of the quantum-corrected mode function is reduced in time, starting from its initial classical (Bunch-Davies) value. This implies that the linear perturbations do not grow; hence, the model is stable. The decrease in the amplitude is in agreement with the system developing a positive (growing) mass squared due to quantum processes. The induced mass, however, remains perturbatively small and does not go tachyonic. This ensures the stability.