Each person has his or her own view as to the importance of the Bunny. It's up to the viewer/reader to determine what they might want to believe about the Bunny's past. This is wonderful and frustraiting for a fan.
It is wonderful in the fact that it lets the reader/viewer form thier own stories with thier own imagination letting thier mind wander unbound by facts. Some thinngs need left untouched to keep a reader's/viewer's intrest. This is one of those things. However, on the flip side, it is frustraiting also because everyone wants to know who's right or how close they were to the truth. Some people would much rather have someone make up the story for them than to come up with one on thier own. It drives some people crazy.
As for myself, I really don't know what to think about the Bunny. It might be something of personal value to Nii from his past. People with harsh childhoods often cling to an item because it gives them somewhat of a safety net or someone to talk to when no one else will listen. The Bunny, obviously, isn't going to start insulting Nii and it could never tell him to shut up.
Also another theory I have seen is that the Bunny could be an item that Nii can control. Being able to control Bunny-sama could give Nii a superiority feeling or make him feel a bit more important. Somewhat like he's playing god.
The Bunny might also be symbolic. It could be symbolic of all the people that Nii controls. Let's face it, Nii is a controling guy. I've suspected several times that perhaps Nii is the one running the show but then again I could be wrong as the story isn't quite over yet and no one is sure what is inside Kazuya Minekura-sama's head. (She loves to torture her fans)
So no matter what theory you might have, Bunny-sama is still quite a mystery much like his owner. We'll just have to wait and see...