We thought Molly only had allergies because she is always very itchy, has ear infections a lot, has hair loss due to scratching and every time we took her to the vet, she was diagnosed with allergies and prescribed antibiotics and steroids and they did help, until she was finished with the medicine, she just kept getting worse. This has been since we got her as an 8 week old puppy! Hypothyroidism isn't rare in Dachshunds but only because of the breeders neglect to their breeding dogs' health and so the disease is passed on to the puppies. We recently took her to another vet and she was diagnosed with possible hypothyroidism (low thyroid) and got her blood drawn and checked and sure enough, that was what is was, she had a really low thyroid, and she is now on treatments (medication) and will be for the rest of her life. If your dog seems to have allergies, and responds to antibiotic and steroid treatments until they are off of them, ask your vet about testing them for hypothyroidism, though we are not glad Molly has this, she will have to be on medication and have blood tests periodically throughout her life, we are glad we now know what has caused this and she is being treated.
Hypothyroidism
What is hypothyroidism?

Hypothyroidism is a disorder of the thyroid gland -- two small butterfly-shaped lobes located in the neck. This gland has a number of functions, but is most well known for regulating your dog’s metabolic rate. In hypothyroidism, the thyroid gland is underactive, and unable to secrete enough thyroid hormone. This, in turn, decreases your dog's metabolism. Hypothyroidism causes a wide variety of symptoms, but is often suspected in dogs that have trouble with weight gain or obesity and suffer from hair loss and skin problems. Many dogs suffer from a low thyroid hormone level for years without treatment. If your dog has chronic recurrent skin problems, she may be suffering from hypothyroidism.
What are the symptoms of hypothyroidism?
How is hypothyroidism treated?

Treatment consists of putting the dog on a daily dose of synthetic thyroid hormone called thyroxine (levothyroxine). There are numerous brand names of this drug. The dose and frequency of administration of this drug varies depending on the severity of the disease and the individual response of the animal to the drug. A dog is usually placed on a standard dose for his weight and then blood samples are drawn periodically to check his response and then the dose is adjusted accordingly. Once therapy is started, the dog will need to be on treatment for the rest of his life. Usually after the treatment is started, the majority of the symptoms resolve.
How is hypothyroidism diagnosed?
All diagnosis begins with an examination and taking of a history. Your veterinarian will be looking for clinical signs of hypothyroidism during a thorough physical examination of the dog, and will ask questions about your dog's health and behavior. If hypothyroidism is suspected, a blood test will be ordered. There are a number of different methods for testing the thyroid. They involve some complicated terminology, but it is important to understand the efficacy of these tests when discussing diagnosis with your veterinarian:
  • Baseline T4 Test or Total T4 (TT4): This is the most common test. Dogs with a failure of the thyroid gland will have a lowered level of the T4 hormone. However, there are other conditions that can cause the T4 to decrease, so if this test comes back positive for hypothyroidism your vet should recommend an additional blood test, either the T3 Test or the Baseline TSH test.
  • Baseline TSH Test: Measures the level of Thyroid Stimulating Hormone. In combination with the T4 or T3 test provides a more complete picture of the hormonal activity of your dog’s thyroid gland.
  • Free T4 by RIA (radio immunoassay): The Free T4 test using RIA techniques does not appear to be more or less accurate than the above TT4 test.
  • Free T4 by ED (equilibrium dialysis): This test may provide more accurate data on the level of T4 hormone in your dog’s bloodstream.
  • Baseline T3 Test: In combination with the T4 or TSH test, these two blood tests can give a clearer picture of the hormone levels found in the bloodstream. This test is not reliable when used alone. The T3 Test should always be given in combination with one of the other blood tests.
  • TSH Response Test: In this test, the veterinarian takes an initial measurement of the thyroid hormones in your dog’s bloodstream, and then injects Thyroid Stimulating Hormone (TSH) into the vein. After 6 hours a blood sample is drawn and the level of T4 is checked. If your dog has hypothyroidism, the level of T4 will not increase even after the TSH is injected. This is an expensive test and is being used less often due to decreased production by the manufacturers.

Info from http://www.thyroid-info.com/articles/dog-hypo.htm
And http://www.peteducation.com/article.cfm?cls=2&cat=1597&articleid=449