I'm not too keen when it comes to tropical community tanks other than cichlids.
Is she the only one getting picked on? You might want to keep an eye out for anyone else getting bullied abit. What kind of tetras do you have? I know certain species have been known to be rather brutal.

I really don't think that your fish are doing this because they are hungry. I only feed my fish once a day and I don't have a problem with tail nipping in any of my tanks.

And to help her feel a bit better you can add a tad bit of aquarium salt to the tank. That always seemed to help bettas that had chewed their tail abit.

Good luck! Maybe someone else will be along soon to give you a better suggestion!