Could possibly be demodectic mange (which is not contagious). It usually starts on the face, front legs, and chest area. A skin scraping would tell if you need dips or not. If it is just localized you may only need a topical creme (by prescription).
Another possibility is flea dermatitis, sarcoptic mange (which is contagious) and caused by a mite, allergies, thyroid problem (but pooch usually gains noticeable weight with this condition). Many, many possibilities but if it is not going away and irritating to the dog definately have it looked at by your vet. Some skin conditions if left to long can cause further internal complications!