We report the recent discovery of three `dying' radio galaxies belonging to the WENSS minisurvey sample: WNB1734+6407, WNB1829+6911 and WNB1851+5707. These sources have been selected on the basis of their extremely steep broad-band radio spectra, which is a strong indication that these objects either belong to the rare class of dying radio galaxies or that we are observing `fossil' radio plasma remaining from a previous nuclear activity. Deep spectral index images obtained with the Very Large Array confirmed that in these sources the central engine has ceased to be active for a significant fraction of their lifetime although their extended lobes have not yet completely faded away. In one case, WNB1829+6911, fossil radio lobes are seen in conjunction with newly restarting jets. We found that each source is located (at least in projection) at the center of an X-ray emitting cluster. We argue that their intriguing association with clusters implies that the pressure of the dense intracluster medium, perhaps a cooling flow, prevents quick liquidation of a fossil radio lobe through adiabatic expansion. On statistical ground we deduce that the duration of the dying phase for a radio source in cluster is one order of magnitude higher with respect to that of a radio galaxy in the field.