Two ideas that could cause this. Cutworms in the soil may be feeding on the stems at ground level. Dig around the plants and see if you can find the thick larvae of the cut worms. You will need to replant your cucumbers but this time surround the seedlings with a still collar made from a plastic cup with the top cut out. The other cause of damage to your cucumber seedlings could be an infection called cucumber wilt disease. Good drainage and good air circulation helps to prevent this disease but there are also cucumber varieties resistant to cucumber wilt if it is a problem in your area. Your local garden center will know what varieties are best. Some gardeners find that making a hill of soil and planting the cucumber seeds or seedlings on a mound helps to keep them healthy. Once your plants mature they will be less likely to suffer from cutworms or disease so don't give up. Keep growing, Marianne Binetti