I think that, for a multicellular organism, this is generally the case, and is especially noticeable at the level of the most complex biological organism that we know of, the human. Senescence seems unavoidable; and seems to entail a degradation of the organism's ability to "successfully communicate" in the meaning of Shannon's theory. When "the center will not hold" — that is, when the meta-information or biological information at increasing rates fails to be successfully communicated to the organism — eventually things "fall apart."
It's avoided by human cancer cells and by human germ line cells. The cellular machinery and organelles of human beings have been working as least as long as there have been humans.