First, is the plant growing in a pot which has good drainage? Is it in a "crowded" spot with lots of other plants round it, some of which also have mildew? If it is, move to a more open position to increase air flow round the plant. Unusual to get mildew on these, more likely to get scale or mealy bug, but I suppose its possible - might be worth spraying with a suitable fungicide for mildew, but make sure by reading the bottle that Chamaerops is not listed as unsuitable for its use.