Answer: Root knot nematodes may be the problem. You could dig a plant carefully and check the roots for the "knots" that are indicative of an infestation. If present, there is nothing you can do for these plants. In the future, grow varieties with a VFN (or VFNT) after the variety name. The "N" indicates resistance to root know nematode.
If you cannot find nematode resistant varieties of a vegetable, try to locate susceptible plants in another uninfested garden spot. When that is not possible, another option is to pick up some used nursery containers (at least 2 1/2 gallon size) and fill them with a NEMATODE FREE planting mix (half compost and half builder's sand is good). Next, sink the pots in the soil (leave about 2" of the pot rim above the surrounding soil so contaminated soil doesn't wash in), and plant seeds or transplants in the pots.
Water and fertilize in the pots as the plants grow. By the time the roots emerge out of the bottom of the pots the plants are large enough and well on their way so the nematodes are not a significant problem.
Another possible problem with your eggplants is southern blight. This is also not cureable on this year's plants. Southern blight will show up as a white fungal mat around the base of the plants. In time, tiny, round, tan structures the size of mustard or cabbage seeds will appear on the surface of the fungal mat.
Locating susceptible crops in another area is the best option for avoiding southern blight. Fungicide treatments are available but should only be used after a positive diagnosis and to protect future crops from infection, not to cure an infected crop.
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