Hi, Butterfly bushes generally don't have too many pests and I've never had anything eating mine. Of course, it would help to know what's doing the damage before you try any type of prevention. Is it a caterpillar? insect? rabbit? etc. Examine the plant closely to see if you see any telltale signs of what's going on before you do anything. Also, these plants grow so fast that it's rare that a pest could keep up. If it were me, unless the plant is being defoliated, I'd not worry too much about it.