Is that rug in the photo new or has it been cleaned recently ? I found this link and has list things that can cause dogs to have allergies and it said allergies to rugs can cause a dog to lose fur. Do you know if any of the other puppies are having the same health issue's? Some people feed their dog according to their blood type when the dog has food allergies. I met a woman that had a DNA test of her dog to see what breed it was as her dog was having food allergies and the woman said it helped her dog .
http://www.drsfostersmith.com/pic/article.cfm?aid=75