Well... we've had one in the fridge for 5 days one time and it was just fine.
Keep in mind that your rabbit is beyond fresh, compared to what you purchase in the grocery store. We put the meat on the coldest shelf in our fridge, which is the lowest shelf for us.
If you pull it out on day 6 or more, just give it the old sniff test... still smell clean? Is the flesh firm and dry,. not dried out but rather clean dry -- not slick? Should be good to go. If something doesn't pass my sniff test it goes out, period.
I understand the question, and the concern. Nothing like something nasty running through your family (sorry, couldn't help myself )
Many butchers will hang pork or beef for a week or longer prior to cutting. As long as the fridge is good and cold, I would worry more about the meat drying out. I don't have any scientific evidence, but I would say 5-7 days as long as it doesn't get dry.