Is the soil too wet? Or too dry?

Can you post pictures of the plants?

If you've over watered then stop watering until the soil is dry and that does not just mean the top layer. Stick your finger in the soil and see if you feel wet. When it is dry water and water deeply then don't water until the soil again feels dry or every couple of weeks. You'll have to water more if it is hot and less when it is cool. Use the finger test until you figure out how much and how often you need to water for your climate.

When you pulled the plants did they have a root at all and was the soil wet down where the roots were. If it wasn't and the plant had a root then you didn't have root rot. If it was dry then you didn't water deeply enough to get to the roots.

Watering deeply and then not watering forces the roots to go deeper and the plant to make more roots. They are looking for water and making a good root structure. Watering daily and not watering deeply keeps the plants roots where the ground is wet resulting in a weak plant with a poor root structure and sets it up for root rot.

All this having been said--If it's overwatering and root rot you'll just have to wait and see if your other plants are infected or if they come back. If it's underwatering then watering correctly should fix the problem.

Are they outside already or are the starts inside? I don't even direct sow my cucumber seeds until June in my zone. Unless your weather is uncharacteristically mild, I'd say they may not be enjoying the cold/damp.

Agree on jumping the gun. I'm just prepping my cucumber bed, sowing seeds in a week or so, and by my standards I'm running a little early.