stem rot?

have you planted them outside recently, as you talk about hardening off?

and to avoid the stem rotting, it is usual to plant them on a mound, so the stem isn't buried, not to plant them deeper, so I'm a bit confused with what you have done with them 

Members of the cucurbit  family don`t like having wet stems, you should always water the compost not the plant.

The way I grow my cukes is to pot on in a bottomless pot which in turn goes into the main bucket filled with both well rotted manure and a top layer of compost, to water I use pop bottles with several small holes drilled around the bottle top, I then cut the base of the bottle off and then fill with water, the stem will always be dry and the roots get the water/ feed they need.
Never a problem with stem rot.

I feel like potting them while feeling sad give them a double distress. always perk them up and pot only when they feel good. sorry to hear that you lost your lot. but remember never over water these plants. water from the tray and not from the top.
its ok if they are dry and look sad
but over watering will make them look bad.

Thought I would bump this thread as I took a photo of my setup that I explained earlier.

So here are my two cucs in thier pots..

I started these by chitting the seed, potted on and then transplanted into the black pot which is bottomless, the big tub is full of rotted manure and the bottles have several small holes drilled in them, about inch and a half down the compost is moist while the top layer is dry as a bone.