Answer: It is difficult to say for sure without seeing the fruit, but it sure sounds like a bacterial or fungal rot. Sometimes the area you mentioned tends to hold water a bit longer after a rain or a sprinkler irrigation. This makes for an ideal environment for bacterial or fungal organisms to thrive in.
While fungicide and bactericide sprays are available, the best solution is to avoid overhead watering (when possible). Sometimes the problem will tend to be bad on year and not the next.
Also, at times a tiny caterpillar will attack at the spot where the stem attaches to the fruit and a rot will soon follow. You might check for a tiny round hole and signs of interior feeding.
For a hands-on diagnosis, you may want to take some fruit to your County Extension Office for a second opinion. Their phone number is 302-831-2506. Jo Mercer is your Horticulture Agent.
Thanks for the question!
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