What would cause holly to drop green berries?
There is some reports that certain varieties will drop or thin it's berries before they ripen to red.
Dragon Lady is one of the varieties know to do this.
Your Holly may also be having pollination issue. It's possible they are getting enough pollen to grow berries, but the process isn't through enough for the fruit to reach maturity.
Plant stress can also cause the fruit to abort. Drought, sudden temperature changes or poor soil nutrition could be the cause.
Water your Holly during hot, dry spells.
I would also have a soil test done to determine the soil nutrient levels and the ph.
Here are some links that will help you.