Most of the demand comes from SE Asia and China where they think this stuff cures medical conditions.
Long term, those governments need to modify primary and secondary school curricula to unambiguously dispel those myths. Eventually, the people who believe rhino horn cures cancer will die out or be pressured by their children, but this will take at least a generation.
In the meantime some species will go extinct. Their only hope is a sudden and prolonged recession or depression in Asia.