Q.Why Are My Seedling Cucumbers Losing Their Root System And Dying After A Few Days.
Seems there is something in the soil that is eating the whole root system, the plant falls over and dies after three or four days. Have planted them twice and the same thing happens. Other seedlings have been planted elsewhere and have survived.

Certified GKH Gardening Expert
If you pull up some roots and examine them carefully, you may see the tiny larvae of the cucumber beetle. Here's an article that should help: https://www.gardeningknowhow.com/edible/vegetables/cucumber/cucumber-beetle-control.htm

Same thing happened to me last year. Read everything. Thought was damping off. Did everything to prevent damping off. Realized I was moving my seedlings outside too early. Temps in 60s and windy. Same seeds, same soil, kept inside, no problems. They may just be too cold? Cucumbers love heat.