In my bathroom I have a stainless steel towel ring and loo roll holder that keep falling off! They seem to be the only type of fixtures available, the ones where you screw bracket into wall, place the main part over the top then tighten the tiny screw underneath. Keep doing this tightening the screw as tight as I possibly can but the damn things still repeatedly fall off the bracket if the kids knock them! Is there any way of keeping them secure?
I know the ones you mean. That little screw needs to be quite tight, and the screwdriver needs to be a very good fit in the screw. In your case it could be that the back plate is distorted. It may help if the plate is removed from the wall, and turned up the other way. Failing that, it is possible to obtain something a lot better, but you will have to shop round a bit.