[hubballi]

This is happening again with quite a few things. Mustard greens, rocket and Kale are two that spring to mind. Healthy growth and then suddenly right at the base of the stem it goes very thin and whispy  until the plant is no more. I found a kale with just a sump and could see where the stem had tapered at he end indicating it had thinned. No slugs or snails or anything else can get to them. It's a mystery 

[bravemurphy]

Sounds a bit like damping off.

[hubballi]

Yes, just looked at  symptoms on wikepedia and exactly he same. Happens every year

[Aunt Sally]

Wikipedia  has a good bit on it:

http://en.wikipedia.org/wiki/Damping_off

Tells you all you need to know.