I have had a asphalt comp shingled roof, that after only three years leached what looked like rust marks. Or to be more specific, it looked like a dumb carpenter nailed up fence slats with regular rusting nails. They bleed rust.
I had discussions with the roofer, the insurance agent and finally had a rep for the shingles come out and determined that a metal by product was introduced into the batch of shingles at the factory and caused rust to emerge from the shingles after the fall and spring rains and cool temps.
the roof was torn off and re done at no charge, even labor was adjusted.
This also happens in concrete too. You have some sort of mineral in the crete and when it absorbs or leaches water, this discolor also comes with it.
As much as I hate to say, I think this is something that you will have to live with. But if your budget does allow, I would rip it up, but me, I would deal with it.