For several years, I've had brown spots on my leafy vegetables and on the leaves of my green beans.
When I went to the co-op garden center this spring, the staff at the garden center said it might be mites. She suggested I do a better job of rotating my vegetables.
After my garden came up, when I see the brown spots, I pick off those leaves. I got rid of infestation in my green beans, but I'm still having some damage on my collards and Swiss chard.
Here's an article on "Organic Ways to Get Rid of Spider Mites." Maybe some of those ideas will work.