Keeping litter alive

Question
Hi Sarah,  I am asking you this because you said you used to be a breeder.  I read some of the responses from some of the other "experts" and well they don't seem to like breeders to much.

I have 4 mini rex does right now which I am trying to breed so I might have a rabbit to take to convention this year.. (and for those who are concerned, no I don't kill the babies that aren't up to par)  I have all of my does in my heated garage which is kept at about 50 degrees.  Unfortunately the last 2 that had kits did it on the day when it was 10 below zero.  The kits all died and I was devestated.  I was told that I can put a lamp above the cage 6 inches above where the next box will be using a 40 or 60 watt lightbulb. I have 2 questions.  I went and bought 4 lamps with clamps and have them set up so the doe cant chew on the cord or the clamp holding it to the cage.  My big concern is will the constant lighting mess up her cycle?  I know rabbits are more active at night but in this climate once the kits are born I am going to need to leave the lights on all the time.  Also, I put the next boxes in at 27 days, should I turn the lights on at the same time?  The last time the kits were born at night and by the time I went down in the morning they had all died from exposure.

Thank you so much, I just have nobody to ask about this and my vet is very helpful but he doesn't actually breed rabbits so his best advise was not to breed them until spring which wont work if I want show rabbits by convention.  

Answer
Actually, if you really want to keep a close eye on the babies, take them away from the mom. I did this with most of my litters, and it works very well. Just bring them to the mom to nurse twice a day (that is all they normally nurse anyway). If she doesn't hop right in to feed them, take her out, put her in the box, and gently hold her in until they have full stomachs. I normally would keep the babies in a shoebox or something else with a lid (with breathing holes of course) so they can't get out and get chilled. You can keep them in the house that way, and keep them in a warm room. It also makes the babies very friendly toward humans, as they associate people with mom.