  We investigate the onset of a not-decaying asymptotic behavior of temporal
magnetic correlations in the Hubbard model in infinite dimensions. This
long-term memory feature of dynamical spin correlations can be precisely
quantified by computing the difference between the zero-frequency limit of the
Kubo susceptibility and the corresponding static isothermal one. Here, we
present a procedure for reliably evaluating this difference starting from
imaginary time-axis data, and apply it to the testbed case of the Mott-Hubbard
metal-insulator transition (MIT). At low temperatures, we find long-term memory
effects in the entire Mott regime, abruptly ending at the first order MIT. This
directly reflects the underlying local moment physics and the associated
degeneracy in the many-electron spectrum. At higher temperatures, a more
gradual onset of an infinitely-long time-decay of magnetic correlations occurs
in the crossover regime, not too far from the Widom line emerging from the
critical point of the MIT. Our work has relevant algorithmic implications for
the analytical continuation of dynamical susceptibilities in strongly
correlated regimes and offers a new perspective for unveiling fundamental
properties of the many-particle spectrum of the problem under scrutiny.
