Did she have them in the nest box or on the wire? If she builds a good nest in the box and lines it with fur, they should be O.K. You just need to make sure they can not get wet and the wind isn't blowing into the nest box. The kits will huddle together under the fur. Unless, there is less than 5 - 6, they should generate enough body heat to stay warm. Now if it gets much below freezing, you may have to bring them inside or provide some type of heat. I have had kits survive down to + 20 F with no problem. I start to have problems colder than that, with new borns. Once they get furred out they can handle even colder temperatures.
Some does feed only once per day. Some will feed as much as five times a day. Ours feed 3 - 5 times a day for the first week.
"This wasn't her first litter, but it was mine, so I will take the blame. How can I keep this from happening again?"
If you have not done so already, talk to the previous owner. Find out if she has a history of eating her kits. If so, cull her. She will most likely do it again. If she has not, give her another chance. She may have biten the kit by accident. Rabbits teeth are sharp and not designed to pick up kits. The kit may have had trouble being born and she may have pulled it out and damaged it in the process.
It's tough to loose a kit, let alone an entire litter. Hang in there, It happens to everyone.
Mike