Why is the emperor called drowsy?

The emperor is a human being who is being contrasted to Yeats's vision of becoming an immortal golden bird, a mechanical work of art. Because the emperor is human, he will experience such human frailties as becoming drowsy. But the golden bird the elderly Yeats dreams of being will never be tired, just at it won't die. Because it won't be tired, it will be able to sing to the emperor and help keep him awake.
The poem as a whole contrasts being a mortal human who grows old and dies to a work of art, which never changes or ages. Yeats expresses a preference for escaping from aging. He does not want to be a "tattered coat upon a stick," which is his image of an old man. He thinks it would be better to be the mechanical bird that never dies or tires.