We talked on the phone with Al from Victoria, British Columbia who has streaks staining his wooden siding. He cleans them off, but they keep coming back.
I think I can safely say that most stains come from too much moisture getting behind the siding and either pushing through the wood and extracting staining substances from the resins themselves, or flowing down the wall behind the siding and then coming out through the overlap in the siding, bringing either grime from the wall, or rust from the nails out onto the surface.
So the real solution is to find the source of that constant excess moisture. The picture Al sent shows a bathroom window right in the area of the stains and it could be moisture from a poorly vented bathroom finding its way into the wall through the window trim or electrical outlets. When I asked him, Al said that the bathroom exhaust fan exhausted into the soffit area just above the bathroom -- Bingo. You cannot run exhaust vents into the soffit area because the hot steamy air will not go outdoors, but will rise back up and cause condensation or frost just above this area inside the attic. In this case I am betting that on cold days frost is forming in the soffit area and up there there is nothing to stop that frost from flowing down behind the siding whenever it melts. This can definitely supply enough water for it to flow down the wall behind the siding and out through the overlap, or through knot or nail holes to deposit the grime on the face of the siding. Move that exhaust duct and you will probably solve the mystery Al.