my cucumbers look sick will they die?

They don't like wet stems.  If you've been watering up to the stem it will die off.

Otherwise, might be mosaic virus - this starts on the leaves.  Or tobacco virus - do you smoke roll-ups in the greenhouse?

That's why I think mine have mostly succumed :cry:  -- even though they were Ridge Cucumbers and I put them on a ridge on my manure heap :!:

PS  :idea: Next time I will plant an empty pot beside the cucumber and water into it instead of on the plant.