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I can only assume that the shrub is not getting the right growing conditions, a picture would help us more if you can get one.
Holly is normally trouble free and I assume that as you are getting fruit (berries) there is a male tree close by to pollinate the one you have (female) other things to cause problems are leaf miners etc but you would see this as the Miner insects bury between the layers on the leaf.
There is either too much watering or too little so dig a bit of soil away at the root area and stick your finger into the soil for either wet soil or dry. Also look and see if squirrels, larger birds etc are trying to carry off the berries.
Some Hollies like an acidic soil and as I don't recognise your one by name, it is worth checking to make sure the growing conditions are right for the type of holly you have as a healthy shrub/ tree that can produce berries, then drops them all makes one think there is a problem with water, feeding, soil conditions or animal.
Hope you can get back with picture or more info re the full name like ( Ilex ????) which will make it easier to identify any known problems with that type.
Good luck. WeeNel.