You need to leave the male flowers on as without them the females don't get pollinated and the courgettes can't grow. I always get a few that go rotten at the beginning of the season and that's because there's not so many male flowers around to pollinate them. They can grow a bit without pollination but then stop and go rotten.

Also don't put a cloche over them as this will stop the insects getting to them to do the pollinating!

Good luck