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There is usually only a few reasons for a dog to walk in a hunched over manner including a disc issue in the back, an anal gland issue, or abdominal pain. As you seem to know with a disc issue, you might see a dog avoid stairs and jumping but that doesn't necessarily mean there isn't a disc problem. Let me give you a site on disc issues in dachshunds.
A dog with an anal gland issue will often also walk with a hunched back to avoid pulling the skin around the rectum. They usually will also hold the tail down. You will want to check to see if your dog's anus is swollen. This may cause a dog to continue to lick the area, possibly drag it The anal glands are 2 sacs on either side of the anus at about the 4' o'clock and 8 o'clock positions. If your dog is continually licking their anus and dragging it, it could also indicate that they are full. This problem can usually be resolved by emptying out the glands. To empty them or express them, you will want to cover the area with a tissue and press your finger on the dog's anal glands with an upward motion. A foul smelling liquid should come out. If nothing comes out and your dog appears to be in pain, you should take him to the Vet. Your vet can do this easily, as he is experienced at it.
Excellent site on anal glands
Abdominal pain is also a cause for a hunched back. Things like stomach ached and pancreatitis will often cause this posture. Usually your dog would probably not want to eat if they had abdominal pain so bad it made them hunched , so this doesn't seem like a likely cause either.
Given his breed, I'd try and get him in to see your vet for a quick checkup.
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