Shipping rabbits is extremely expensive and time consuming.
When you ship rabbits, you must take them all to the vet to get a certified document from the vet proving that your rabbits are not carrying diseases. No airline will allow you to ship rabbits without this certificate of health. This alone, can cost you a pretty penny.
Next, you must contact your local airlines and find out which planes will allow rabbits. Not all airlines will ship live animals and the ones that do ship them, may only accept it during certain times of the year so as to avoid exposing the animals to extreme temperatures.
When you do find an airline and a good time to ship your rabbits, you'll have to paythe costs of the shipmentweeks, sometimes months in advance. You'll also have to pay for properlly designed shiping cages and feeding equipment for the rabbits. The airlines will not allow you to use just any type of cage to ship your animals in. Sometimes you can purchase these cages directly from the airlines, other times you can purchase them from rabbit supply warehouses.
Once you have paid for the shipping costs and the specially equiped cages, your total is going to look around $200-$300, for a single rabbit to be shipped. The more rabbits you ship, the more expensive it's going to be for you. Don't forget the cost of gas that will be needed to take the rabbits to the air port as well.
On top of all of this, no airline will guarantee the health of your rabbits while they are being shipped. This means, that if your rabbits die from stress, extreme temperatures, lack of proper oxygen, cramped storage, or some how become injured during the flight-it is not the airline's responsibility and you'll still have to pay the costs of the shipment. And trust me, these kinds of things happen far too often...
So, all in all, for these above reasons, this is why most breeders choose not to ship rabbits. It's just far too expensive and stressful for both the owners, purchasers, and rabbits.