Demodectic mange is an opportunistic infection because the immune system is weak. I would bathe with DEFENDEX shampoo once or twice weekly for 4-6 weeks or a couple of weeks past having a negative skin scraping. The shampoo is very concentrated so just use a small amount. This is a less toxic approach than the conventional dips.
I would also use the homeopathic DERMA-IONX both internally and externally to heal and soothe the skin as well as rebuilding the immune system. Giving probiotics, vitamin C, and Omega 3,6,9 will all help in that goal. DERMA-IONX also helps the body to better utilize the supplements for faster results. I would start with a 1/2 dose of DERMA-IONX twice a day. It is easiest to add it to the food. I would feed a grain free dog food. I would offer filtered drinking water to avoid chlorine or fluoride. It would also be good to bathe with filtered water. If you have chlorinated water getting a filter would be helpful.
This would be a safe option to deal with your problem.
Please let us know how you progress or if you have any other questions.