Sorry to hear about this. Can you send in a pic? It would definitely help, as would taking a leaf in to your favorite nursery. It might be a fungus, and it might be insects of some type, like scale--can you scrape off the black stuff? It could also be mold forming on the droppings of aphids or scale--they excrete sticky waste ("honeydew") that often grows mildew mold on it. Is there a chance the plant has an infestation? Or an overhanging/nearby plant does??

Just some thoughts. I'd take the leaf in to a nursery. You could get some fungicide if it's a fungus (and make sure the tree gets plenty of ventilation which fungus hates) and if it's an insect, you could get some systemic insecticide for it too.

Let us know what you do and how it works out. I love fan palms so I really hope yours is okay.

Take care,
Grant