When one is tired, their butt muscles are not fully in tune with the rest of the body, and, therefore, tend to sag or droop from their usual, flexed position; the "nappy" referring to the tired state of said person, and the "tail" referring to said person's rear end.
"Boo, get your nappy tail back to bed!"
"Dang, you're droopy! That's one nappy tail you've got there!"
"Dang, you're droopy! That's one nappy tail you've got there!"
by @Mr.Toashty March 1, 2017