  A tidal disruption event (TDE) occurs when a star is destroyed by the strong
tidal shear of a massive black hole (MBH). The accumulation of TDE observations
over the last years has revealed that post-starburst galaxies are significantly
overrepresented in the sample of TDE hosts. Here we address the post-starburst
preference by investigating the decline of TDE rates in a Milky-Way like
nuclear stellar cluster featuring either a monochromatic (1 M$\odot$) or a
complete, evolved stellar mass function. In the former case, the decline of TDE
rates with time is very mild, and generally up to a factor of a few in 10 Gyr.
Conversely, if a complete mass function is considered, a strong TDE burst over
the first 0.1-1 Gyr is followed by a considerable rate drop, by at least an
order of magnitude over 10 Gyr. The decline starts after a mass segregation
time-scale, and it is more pronounced assuming a more top-heavy initial mass
function and/or an initially denser nucleus. Our results thus suggest that the
post-starburst preference can be accounted for in realistic systems featuring a
complete stellar mass function, even in moderately dense galactic nuclei.
Overall, our findings support the idea that starbursting galactic nuclei are
characterized by a top-heavy initial mass function; we speculate that
accounting for this can reconcile the discrepancy between observed and
theoretically predicted TDE rates even in quiescent galaxies.
