Answer: Based on your description I am not able to tell you exactly what is happening, however it might be a case of mechanical damage to the stem or possibly bacterial wilt infection, a fairly common problem. The following article shows photos and detailed information about this. You will probably need to cut and paste the complete url into your browser to make it work correctly.
You might also want to consult with your local Penn State county extension to obtain a more specific diagnosis. I'm sorry about your cucumbers!
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