Flowers on Courgettes Look Snapped Off?

I have a similar problem to the zucchini flowers post, and you are suggesting that animals or pests could be responsible. I have 1 courgette (think this is the same thing) which is healthy and keeps flowering huge orange blossoms. They open, stay like that for a couple of days, then when I go back to look, they have been snapped off where the flowers joins the stems. It can't be pests or animals, as its growing in a very small greenhouse/lean to and the other stuff in there is fine.

I looked for bugs and stuff and there is no sign of anything like that. It's as though someone is coming in at night and snipping the flowers off and all I am left with is a long stalk.There are about 9 more flowers to come, I have lost 4 so far. No-one can access my garden so what am I doing wrong? Please can someone help before I lose the whole lot :)

By Mary N.