We have an abridged version of The Velveteen Rabbit and I don't remember ever reading the original version, so perhaps this is addressed in that. I doubt it.
In our version the rabbit gets thrown away because the boy gets sick and the rabbit is so sad he cries. Then a fairy turns him into a real rabbit. Well, every time we read that I can't help thinking that the velveteen rabbit then hops off into the woods and promptly gets torn apart by a wolf, because it has absolutely no real-world survival skills.
I guess I'm not sentimental enough.