Avernus, I'm so sorry about the kitten dying. That's so hard to take. However, it may have had a birth defect. Was the doctor a vet? Are mother and kittens separated? I'm not quite sure.
Have you been bottle feeding, tube feeding, or is mother feeding them?
If you are feeding them, please be careful not to allow the milk to flow fast. The kitten could choke on it and it could go down into the lungs. If you have not consulted the vet, please do so. Even if the mother has no milk (a vet will tell you) her mother love would be helpful.
Could you go into more detail? Your cat might be too young, On occasion the kittens are not strong or big enough to survive. Use your vets advice on how many cc's of kitty formula to use. Do not use cow's milk out of a bottle. Buy a can of kitten formula at a pet supply store or at the vet's.
Of course, mother's milk is best. Good luck. Keep us informed!