  The phenomenon of ergodicity breaking of stochastic dynamics governed by
Generalized Langevin Equations (GLE) in the presence of well-behaved
exponentially decaying dissipative memory kernels, recently investigated by
many authors (Phys. Rev. E {\bf 83} 062102 2011; Phys. Rev. E {\bf 98} 062140
2018; Eur. Phys. J. B {\bf 93} 184 2020),
  finds, in the dynamic theory of GLE, its simple and natural explanation,
related to the concept of dissipative stability. It is shown that the
occurrence of ergodicity breakdown for well-behaved dissipative kernels falls,
in general, ouside the region of stochastic realizability, and therefore it
cannot be observed in physical systems.
