You could use hackneyed, pronounced /ˈhæknɪd/. Here are two of the OED’s senses for it:

2. Used so frequently and indiscriminately as to have lost its freshness and interest; made trite and commonplace; stale. 3. Habituated by much practice, experienced; sometimes with the ulterior idea of disgust or weariness.

Hackneyed is especially appealing due to its obvious derivation from hackney, a word used since Chaucer and before for equines of a middling nature and which later were used for equines available for hire, as in a hackney horse, hackney ass, hackney mule, all given by the OED. Using the word hackneyed lends connotative weight to the sense of something that’s now in a bad way as a result of having been used so much over its lifetime of service.

For alternatives, there is also the compound adjective time-worn, which per the OED means:

Worn by process of time; impaired by age.

For simpler terms, you could also turn to tired, worn-out, run-down, or broken-down work just fine as well.  Decrepit might work too, but probably not *dilapidated except in figurative use.

You could use hackneyed, pronounced /ˈhæknɪd/. Here are two senses for it:

2. Used so frequently and indiscriminately as to have lost its freshness and interest; made trite and commonplace; stale. 3. Habituated by much practice, experienced; sometimes with the ulterior idea of disgust or weariness.

Hackneyed is especially appealing due to its obvious derivation from hackney, a word used since Chaucer and before for equines of a middling nature. It was later were used for equines available for hire, as in a hackney horse, hackney ass, hackney mule, all given by the OED. Using the word hackneyed lends connotative weight to the sense of something that’s now in a bad way as a result of having been used so much over its lifetime of service.

For alternatives, there is also the compound adjective time-worn, which means:

Worn by process of time; impaired by age.

For simpler terms, you could also turn to shabby, tired, worn-out, run-down, or broken-down. Those should work just fine as well. Maybe even disused (but see below for the noun desuetude).

For longer, more Latinate terms, decrepit might work too, but probably not dilapidated except in figurative use since it has no stones to lose. The uncommon noun desuetude in common use means:

The condition or state into which anything falls when one ceases to use or practise it; the state of disuse.

And has come to have a legal meaning as well. But if you write that your donkey has lapsed into desuetude, many readers will have to look the word up. :)

_{All definitions taken from the OED.}