The black mildew is more of a health hazard than a hazard to the wood. It should be killed off using a bleach-detergent solution (don't use a detergent with ammonia - generates toxic fumes). This will kill the mildew and the surface should be cleaned and painted with a primer and top coat containing a mildewcide. In areas with extreme mildew problems (warm and humid) the primer should contain a zinc oxide for longer lasting effect.