Answer: If they are disappearing, it could be an animal eating them overnight. To prevent that, try forming a protective cage of wire mesh over top of the plants.
If it is a disease problem, you might want to take care to add ample organic matter to the soil and to rotate the planting so that you are not planting cucumbers where cukes, zukes, melons, or squash have been grown in the past several years. This would help reduce the change of infection through the soil.
Finally, if it seems to be a pest problem, you can try covering the plants with a summer weight fabric row cover to exclude insects which may either damage the plants or transmit diseases when they contact the plants.
I hope this helps you troubleshoot.
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