Green’s Dictionary of Slang

sleepy adj.1

[see cit. 1796]

old, worn-out.

[UK]Grose Classical Dict. of the Vulgar Tongue ms. additions n.p.: Sleepy. Much worn: the cloth of your coat must be extremely sleepy, for it has not had a nap this long time.
[UK]Grose Classical Dict. of the Vulgar Tongue (3rd edn) .
[UK]Lex. Balatronicum [as cit. 1796].
[UK]Egan Grose’s Classical Dict. of the Vulgar Tongue.