You might be experiencing a condition known as 'damping off.' That's a fungal disease brought on by moist damp and/or unsanitary conditions. It causes young seedlings to collapse almost overnight. Cucumbers seem particularly vulnerable as they are to all kinds of plagues. You should find a way to reduce the moisture/humidity. Don't transplant into cold wet soil & not too close together. Don't over water, keep the seedlings just barely moist with good drainage. Keep a window open if it's not too cold outside, getting good air circulation/ventilation. Get the air moving around your seedlings. A low powered fan blowing air around them will help.

I suspect it is a form of root rot too. I usually sow one seed per 3" pot. when roots are just coming out the bottom they are moved on into 6" pots. I let the compost get to the same temp as the plant.
[I was amazed at the temp difference between the plants on the staging and the compost under the staging]

I fill the 6" pot with compost with an empty 3" pot in side it so the planting hole is the identical shape of what the plant is in. then take out the 3" pot, knock out the plant pop it in the hole in the 6" pot and tap the pot on the staging to settle compost. then they are watered from the bottom and left to get on with it. I do this with all plants grown on in cells/pots to avoid unnecessary root disturbance.

I also find fluctuating temperatures cause them to wilt, we've had a couple of early morning frosts and warm sunny days

that's true. I was ready to make pickles, until I had an issue with downy mildew. It wiped out my whole crop overnight. I always plant more plants then I think I need. I'm just happy if I get a few edible cucumbers.

Yes, they definitely don't like fluctuating temperatures at that stage, and nothing under a steady 15 degrees or so. Mine stay on a bright (but not sunny) windowsill indoors until they're a lot further along.