Posted: 14/06/2014 at 10:34
Not a disease - really it's not
It's early in the season and temperatures may have a lot to do with it, not many insects about etc. Sometimes the baby courgette appears to grow a bit but hasn't really been pollinated so then rots away. I'd have a go at the manual pollination if I were you.
Also, as they're in pots they're susceptible to drought and the compost does look a little dry in your photos. They don't need to be soggy, but they do need keeping an eye on the moisture level.