Hello steveb. Perhaps it's always a problem with oak which lives outdoors. Perhaps drying the oak before using it doesn't get rid of the tannin which has to leak out in the end. Presumably it will stop at some point, when there's no more tannin left....
I have made my porch canopy, with strips of dpm under it, long enough to reach the ground, which will catch the oak-juice before it stains the render.
I've never tried this myself (so no guarantees), but I have heard that washing raw oak with a solution of baking soda can reduce its tannic acid content (makes sense really, since baking soda is alkaline). However, I imagine that you'd have to wash it many times to stand any chance of reducing the tannins to the point where they won't dissolve in water and cause stain runs.
Out of interest, I expect you know that tannins from oak bark were used for tanning leather. Tanna is an old German word for oak.