Antifungal agents fall into (at least) 2 general categories: topical treatments and systemic fungicides. I would recommend considering both alternatives if you have ruled out insects as a causative agent, and are unable to find the characteristic signs of mites. Many antifungal agents describe themselves as most effective (if you read the fine print on the instructions) as preventive agents, ie. something you apply to the plant every 7-10 days (assuming it doesn't rain) before the situation gets out of control. In theory the systemics (azole fungicides, generally) confer upon the plant some kind of inherent immunity to fungal attack, once they have been taken up and transported by the plant. Finally, it is generally recommended to not rely on one agent alone for control, rather alternate between 2 or 3 different ones, so the fungi (smart little eukaryotic bastards) don't acquire resistance.
