According to Hessayon -
Withering of young fruit (stop growing when they are only a few inches long and withering spreads back from the tip) has many possible causes, such as draughts, heavy pruning, using fresh farmyard manure. Most likely reason is faulty root action due to poor drainage, over watering, poor soil preparation. Remove damaged fruit and spray with a foliar feed, withhold water and ventilate the greenhouse, but keep floor damp as usual.
Maintain steady growth by careful watering.
I had withered cucumbers to start with a few weeks ago (also part of the cucurbit family) which was because they were in a pot with no drainage. I drilled holes in the bottom and let loads of water out, and today ate my first cucumber, very sweet and juicy.