At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
I'd wager that one reason is by the accumulation of mutation.
From a perspective of time - a cell or organ that is older simply has had more time for damaging mutagens and UV radiation to take their toll on the DNA. It's more probable for an older cell or organ to have such mutations occur in a vital part of the genome, which may render defenseless against certain pathogens.
One would think that such mutations would be selected against, and weeded out given a decent amount of time. This is not always the case. In the context of an organism - evolutionary pressures are weaker as the organism gets older, because it also becomes less likely to reproduce. Detrimental mutations build-up simply because they are no longer passed on, and thus cannot be selected against. These mutations, which manifest themselves when the organism is old, persist in the gene pool. This approach incidentally comes from Medawar's proposed theory on why we age.
kma230 gave a very good answer. I'd like to speculate that an aged organ has less ability to repair itself due to lower numbers of stem cells.