My dog's private parts infection isn't healing. Why isn't he better?

Poor pup. For any wound in which it doesn't heal with broad spectrum antibiotics you will need to get the area cultured or surgically removed. I assume he is intact, so a neuter + scrotal ablation (removal of the testicular sack) are recommended for this problem. However he unfortunately sounds very ill and potentially may have something else underlying that is causing this, such as Brucelosis, a fungal infection, or systemic infection. He need bloodwork analysis and perhaps even titers ran to check for these things before surgery. Having him hospitalized also should be considered to provide him supportive and nutritional support. I hope Rocky gets well soon and best of luck getting to he bottom of his illness. Take care.