We present experimental results on the robustness of acoustic time-reversal focusing in a multiple scattering medium undergoing perturbations. Time reversal in such a medium can be viewed as a correlation technique, analogous to diffusive wave spectroscopy. Moreover, the recent introduction of telecommunication techniques based on time reversal in changeable media naturally raises the question of sensitivity to a perturbation of the medium. We consider the situation where the reversibility of an acoustic wave generated by a linelike source is gradually destroyed when a perturbation is added, either locally (by removing scatterers) or globally (by changing the temperature) to the multiple scattering medium.