I can't be sure what caused the death of your cucumber plants based on that description alone. It could be that they need additional water or that the roots were burned with fertilizer applications that work to the excessive. It could also be that some type of soil fungus or insect is damaging the plants.
Since you had a plant that looked fine and suddenly began yellowing I suspect there is a root problem involved. If the plant continues to go downhill you might note when you pull it up what is happening in the roots. Is it an insect (areas of the roots chewed away), swollen areas on the roots (nematodes), or do the roots look rotted?
I realize this doesn't save your current plant but without knowing the cause it is hard to prescribe a cure. When you discover what is causing this problem then we can help provide suggestions for preventing it from happening to future plantings.
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