  Recently Song {\it et al}., Phys. Rev. A {\bf 80}, 012331 (2009), have
discovered that certain two-qutrit entangled states interacting with
multi-local decoherence undergo distillability sudden death whereas their
locally equivalent states do not exhibit such behavior. We have found that
their basic equation of motion missed some terms and therefore the subsequent
calculations and conclusions are not correct/valid except that distillability
sudden death may occur. We provide the missing terms and point out the
corrections which must be done in the literature to remove confusion. Moreover,
we have studied this feature for certain entangled states under global,
collective and multi-local decoherence. We have found that entanglement sudden
death and distillability sudden death may happen under global and multi-local
noises. Moreover, local unitary transformations can not avoid distillability
sudden death.
