Hello, I'm Dr. Kara. I have over 20 years of experience as a veterinarian and I'd like to help with your concerns about Jake and his skin problem.
I think that you are referring to sarcoptic mange when you ask about "fox mange". This is a highly contagious mange mite that can be passed easily from dog to dog or even other mammals such as yourself. If all contact animals aren't treated he will continue to be affected. As well there needs to be treatment for a long enough period so that the eggs hatch and the new mites are killed. We usually need to treat for a good 2 to 3 months in some cases but at least 6 weeks in most cases.
I understand that veterinary costs are expensive but there isn't any effective over the counter treatment for sarcoptes. I would discuss using Advocate (a topical medication that is also effective for flea and heartworm control) every 21 to 28 days for several months with your veterinarian or ivermectin injections every 2 weeks for at least 3 treatments. If you have more then one pet I do recommend that they are all treated because there are asymptomatic carriers that can keep infecting your pup.
I suspect in your pup's case he simply wasn't treated for a long enough period or he is continuing to come in contact with the mites are getting reinfected.
I know that you would like to hear that there is something effective that can be done for him at home with an over the counter medication but that simply isn't the case. I don't want to mislead you and let you think that there is effective home therapy, especially as sarcoptes is infectious to you as well.
Best of luck with your fellow, please let me know if you have any further questions.