In the early 1970's, we were stationed in Germany and adopted a dachshund puppy. I took her to a German veterinarian, who had been recommended as a dachshund specialist because she had floppy dew claws on her hind feet that needed to be removed as they would catch on the carpets and hurt her. After her operation, the veterinarian pointed to a bare patch on her tail and told me she had "leather tail." He suggested that I give her cod liver oil orally and also to put a small amount on my finger and rub it into the bald place on her tail. Trust me, a dachshund with fish breath and a fishy smelling tail is not pleasant, but I faithfully gave her cod liver oil on a spoon, she would lick it clean, and rub a small amount on her bald patch. By the time she was about 6 months old, the bald patch was covered in hair, and thankfully I could stop with the cod liver oil treatment.
Flash forward to 2009. I took my current dachshund, Libby, to a dachshund festival. Games, races, and prizes and lots of fun until another dachshund, who was off his/her leash ran at Libby and bit her on the top of her head. We cleaned the wound and I applied neosporin until it healed. There was a bald spot about the size of half a dime that just wouldn't grow hair. After a couple of months, I decided that the biting dog must have removed some of the skin that grew hair, but then I thought, it wouldn't hurt to try cod liver oil. After about four months of dosing Libby with a spoon daily, she loved it, and rubbing a dab on top of her head, hairs started to grow in. The up side of this treatment is that it seems to help grow hair, the downside is that your dog is pretty much socially unacceptable as far as odor goes while going through the treatment.