A long time. The origin here is disputed. Some say it is a rhyming term for donkey’s ears, which are quite long, and possibly also a punning allusion to the Cockney pronunciation of “years” as “ears”; others believe it alludes to donkeys being quite long-lived. The expression dates only from the late nineteenth century. Edward Lucas used it in The Vermilion Box (1916): “Now for my first bath for what the men call ‘donkey’s years,’ meaning years and years.”