Earwigs are common culprits, as are snails.
Use pellets or insecticide to cure the problem.
In my own garden its earwigs that munch through them.

I've had the same problem, and I've put slug pellets down, which didn't stop whatever it was, so I'll have a look for earwigs next! Thanks Louise. I did wonder whether it could be those perishing vine weevils again!! They do such a lot of damage, because the grubs eat the roots and the beetles eat the leaves!! I'm going to have a dig around in the soil underneath the plant to see if I can find any grubs---fat, white things with a brownish head, and if I do, they won't last long!! Good luck, Annie (Cumbria)