We investigate the bright cut-off of the PNLF, that has been suggested as a powerful extragalactic distance indicator in virtue of its observed invariance against populations effects. Theoretical PNLFs are constructed via Monte-Carlo simulations of populations of PNe, whose individual properties are described with the aid of PN synthetic models. The basic dependences of the cut-off magnitude M* - age of the stellar progenitors, metallicity, transition time, and nuclear-burning regime of the central stars - are then discussed. We find a serious difficulty to explain the age-invariance of the cut-off brightness over an extended interval, say from 1 to 13 Gyr, that observations of PNLFs in galaxies of late-to-early type seem to suggest.