Oh RATS! The cause is now obvious.

Good morning everyone,   Rugoso di Cosenza giallo

well I bit the bullet and pulled up the melon plants that had suddenly/gradually wilted and died in the greenhouse.  I hope you can see what I saw.  The largest melon was a good 5" long.
The roots have been completely eaten away
First I'll trace the cause and then figure out a method of growing them in pots in the greenhouse where there is no way of anything climbing into those pots.

Cheers,  Tony.
 P.S. I have courgettes and cucumbers doing very well in the greenhouse within inches from the (deceased) melons...