An old thread I know - but rabbits, certainly pet rabbits, pair up for life and once the bond is there they should not be seperated unless they have to be. After seperation or the death of a partner, there are thousands of documented instances of the remaining rabbit dying in short order, as mentioned above. Despite the scientific evaluation, its pretty clear that they die of a broken heart. Sometimes a rabbit will bond with new partner but often they don't really.
Pet rabbits should not be kept alone and bonded pairs should not be seperated. As mentioned above, they don't like being picked up really, this applies more as the rabbit breed gets bigger. Big rabbits really are not suitable for picking up all the time and rabbit ribs are easily fractured. Some will bite if you annoy them, our largest rabbit has never bitten and is the most placid (and the most intelligent) but I would not try and pick him up, rather let him jump up onto my lap. If you want a pet you can pick up a lot, get a cat!