Do you notice this starting on your lower leaves and working its way upward? I get that disease on my tomatoes and my local gardener friend gets it, too. He says it is a soil borne organism that causes it, so we should protect our plants from getting splash back from rain or hose watering. We do that by putting a layer of wheat straw under the area. He also pulls the lower leaves from the plants as they grow even before any signs of the disease show! I remove the lower leaves as they start to show the disease, but I'm beginning to think my friend's more drastic measures are better. He does get much heavier fruit bearing, despite us both using seed that he germinates.
The wheat straw under the plant to keep splash back from going on sounds very smart. I have been spreading grass clippings under my veggies that are planted in the dirt and it has really helped with weeds and the grass seems to provide a dryer surface than the dirt. I think I will do the same with the ones in pots. Not straw, but grass just the same, right? I like that tip.