For those who can't succeed because the cat keeps disappearing:
If you put the cat in the box and then give it the yarn ball, a second cat will appear so if you loose him you have an extra cat. If you want the cat out of the box you have to click and hold the box and shake it a little bit until the cat jumps out (this also works on all the other cat interactions)
 "Youda Survivor"){kind=icon}
 "Soul Mirror"){kind=icon}
 "Doodle Cat"){kind=icon}