Hi Karen
I am growing some of my cucumbers in pots for the first time this year because of lack of space. One of my pot grown ones is showing the same stem rot as on yours. I believe it is overwatering the pot in my case. Never had a problem with cucumber stems rotting when I’ve planted in the ground. All my other pot grown look ok but they are in a slightly sunnier spot than the one with some stem rot. I too will ease up on the watering. Courgettes, apart from being a little wind battered, are doing great in pots but then they grow faster than the cucumbers and need the water. I tried to raise the soil a little in the middle of the pots when I planted and I water around the rim mainly.
Eliza