On the missing second generation AGB stars in NGC6752

[Abridged] In recent years the view of Galactic globular clusters as simple stellar populations has changed dramatically, as it is now thought that basically all GCs host multiple stellar populations, each with its own chemical abundance pattern and colour-magnitude diagram sequence. Recent spectroscopic observations of asymptotic giant branch stars in the GC NGC6752 have disclosed a low [Na/Fe] abundance for the whole sample, suggesting that they are all first-generation stars, and that all second-generation stars fail to reach the AGB in this cluster. A scenario proposed to explain these observations invokes strong mass loss in second-generation horizontal branch stars possibly induced by the metal enhancement associated to radiative levitation. This enhanced mass loss would prevent second generation stars from reaching the AGB phase, thus explaining at the same time the low value of the ratio between HB and AGB stars (the R_2 parameter) observed in NGC6752. We have critically discussed this scenario, finding that the required mass-loss rates are of the order of 10^{-9} Mo/yr, significantly higher than current theoretical and empirical constraints. By making use of synthetic HB simulations, we demonstrate that our modelling predicts correctly the R_2 parameter for NGC6752, without the need to invoke very efficient mass loss during the core He-burning stage. Our simulations for NGC6752 HB predict however the presence of a significant fraction - at the level of about 50% - second generation stars along the cluster AGB. We conclude that there is no simple explanation for the lack of second generation stars in the spectroscopically surveyed sample, although the interplay between mass loss (with low rates) and radiative levitation may play a role in explaining this puzzle.