When I was in Vet school we always had four or five Dachshunds "walking" around the clinic in their little wheeled carts. They were recovering from a condition called Intervertebral Disk Disease which is common in the breed. As many as twenty percent of Dachshunds will succumb to IVDD at some point in their life.

The disease is the result of rupture of the intervertebral disk. These disks are kind of like shock absorbers between the vertebral bodies. They contain a hard outer covering and a fluid filled center. Injury or age related damage may result in rupture and leakage of the disc contents up into the space occupied by the spinal cord.
When that happens the result can be partial to complete paralysis. Now there is new hope for these dogs.
Work being done at the Vet College at Texas A&M has resulted in a new treatment for dogs affected with IVDD. This research may also apply to people with spinal cord injuries in the future.
The research involves a drug that blocks the formation of a protein that forms in response to spinal cord injury. It is this protein that is responsible for much of the ongoing inflammation and damage to the cord beyond the original injury.
When a disk ruptures the initial damage is responsible for the immediate clinical signs of pain and paralysis. The longer lasting damage and the degree of permanent loss of function is often due to post injury inflammation, swelling and the resultant damage. If the inflammation can be brought under control by medication, and sometimes surgery to relieve the swelling, the cord can recover. How quickly the inflammation can be relieved is critical to the long term prognosis.

Dachshunds, Welsh Corgi's, Basset Hounds and a few other breeds are more likely to suffer from IVDD due to their long backs. Being long and short puts lots of stress on their lumbar vertebrae. If you have one of these breeds make sure that you discuss the signs and symptoms of IVDD with your Vet.
For a more complete discussion of this condition see the attached article on the subject.