Actually what your cotoneaster is doing is a very fine thing indeed. The reason for this is that any berries remaining on the plant may develop fungal growth on them such as fireblight and if your plant becomes infected with this or another damaging fungus it will be in big trouble. For the same reason I suggest that you remove any dropped berries or leaves from around the area.

What kind of Cotoneaster is it, Chloro? The berries of some species last longer than others.

Is it planted in a dryish spot? Dryness at the root could be causing this, but it would be useful to know which variety of Cotoneaster it is...

It's Cotoneaster Horizontalis. I made sure it didn't dry out by watering it once or twice a week in summer. Thanks.

I think it is more likely to be dryness too. watering once or tice a week may not be enough. how long have you had it in your garden?

C. dammeri is the one we grow here, and we rarely water it more often than twice a week, even here in the desert. We do generally put a good 40-80 liters on at a time, though. Twice a day needed in containers, though, and I don't think Chloro specified where it was planted.

My Cotoneaster horizontalis bonsai holds its berries throughout winter but only if the blackbirds don't get them first.
Its about 28 years old lives in a shallow (1"deep) container and is also planted on a rock. It once dropped its berries early but that was my own fault due to mis-watering (not enough).

Sounds like dryness - the time when people often mismanage watering, or don't realise its necessary, is autumn, in particular, late September and October. If the weather isn't damp and there's a fair amount of sun about, plants still dry out and still need watering, if they've not been in the ground longer than 3 or 4 years, or if the soil they're in is light.

Thanks to everyone who has been commenting. My cotoneaster is in clay soil in the ground and it's been there for about 3 years. I didn't realise though that I needed to water in autumn. Maybe that's been the problem.

Worth checking this autumn - specially if you live in a warmer part of the country and the shrub's in sun. I was still watering pots on the balcony at Christmas this year...