I speculate you're dealing with a fungal attack, potentially weakening the plant to allow bacterial infections as well.
Fungi thrive in warm, moist conditions, and are usually spread by water-borne spores. If your plants are in contact with each other, or you get any splashing between plants when watering, then that's the likely spreading vector.
I would recommend a 3-pronged approach:
- Treat the plants with a systemic fungicide like Cleary's 3336WP (thiomyl)
- Spray your growing area with a topical disinfectant. I recommend Oxidate (AKA Biosafe Disease Control) for in-home applications.
- Improve your conditions to avoid the pathogen sharing vectors and increase air flow.