It leaves on the second night. If you are lucky enough to stay awake till midnight you will see it leave.
:furawatchi: It is too sad *cries*
Anyway, I tried staying up until it left, but fell asleep at 11.59pm! Noo!
So don't try it.
But my lucky dad was awake to see it...
If you want your Tama to stay for longer, pause it at night.