It is possible you have Early Blight. Mine do the same thing. They will be fine until the first full day of high heat and humidity then it just explodes. The first thing to do is get all the bottom leaves trimmed off - I've read that it is fine to take everything off at least the first foot of your plants and even up to 18". Get them in the trash then wash your shears and gloves with bleach. This will help stop the spread. Copper fungicide or Daconil sprays, or Epsom Salt drenches are usual recommendations. I usually start spraying mine about 2 weeks after planting. Good luck with yours.

Your plants may have fungus.