Answer: Based on your description it sounds like a problem with bacterial wilt or borers. Wilt is spread by cucumber beetles, so controlling them will go a long way toward helping the problem. To stop them, cover the plants with a summer weight row cover which will exclude them. Unfortunately, this means you will need to hand pollinate or open the cover occasionally for pollination to occur.
Borers tunnel into the vine usually near the base and you can actually see the hole or might notice the "sawdust" on the ground near the hole. These can be carefully removed from the vine using a sharp knife to make a slit where the borer is. Then bury portions of the vine at the nodes to try to cause it to add more roots so it can support itself and recover despite the damage.
Additional steps would be to clean up and discard all plant debris in fall and as it occurs during the summer, turn over the soil in fall and spring to expose any overwintering pests to the weather, and be absolutely sure to rotate your crops so that melons, squash, pumpkin, cucmber and gourds are not grown in the same location more often than at least every three years.
In the event it was not bacterial wilt or borers, but another problem, the same prevention measures would apply with the exception of the row cover. If it happens again this year, you may want to take a sample and/or photos to the county extension (473-2540) for a definite diagnosis and suggested remedies.
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