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I will try to add to my colleges answer with more possibilities that may help.
There are many reasons for chronic licking by dogs. First I would say an allergic reaction following exposure to antibiotics applied to the skin; metals (nickel?); materials such as rubber, wool, and plastic; or chemicals (dyes and carpet deodorizers) or inflammation caused by irritating substances such as poison ivy.
If none of these sound like a possibility self-licking in dogs results in self-trauma; possible causes include anxiety, boredom, stress (e.g., new member in household); licking can develop into an obsessive behavior. Treating this would mean relieving the underlying cause, restrict licking by using an Elizabethan collar with use of behavior modifying medication.
Another option since it is a dashund would be Acanthosis Nigricans. This is a genetic condition found in Dashunds and is noticed by itchy dark areas. Since you said your Daschund is dark skinned, it may be tough to see? I have offered a link to a site to explain it better than me paraphrasing.
Hope this adds to Jane's offerings and together we have assisted you.