Yes birds of prey can be a risk to small pets (and children!).
When we have our rabbits out in the yard we are always outside with them. As this video shows even a terrier on a leash surrounded by people is at some risk.
Other images of dogs and cats being attacked by birds of prey can be found on the internet. From these images it seems that animals in the 7 pound (3kg) range are at risk from birds of prey. How big does a pet need to be, in order to be relatively safe from attack by birds of prey?
The following images may be disturbing to some, mouse over will display them.
The size of pet that can safely be left outside unsupervised depends on the size of predators in your area, as well the amount of protection that you have to keep predators out of your pets area.
If you leave your small pet outside unsupervised, you presumably have a fence to keep feral/neighborhood dogs out as well as yours in. You need to be aware of all the predators in your area, some like racoons can climb fences and occasionally attack cats and even dogs (rarely).
Some flying birds of prey like Eagles can carry off animals up to half of their body weight. Some source recommend that pets under 15 pounds (7kg) never be left outside unsupervised. I did not find good references for birds of prey eating dogs, I did find reliable references of them catching and eating foxes, it is not difficult to image that dogs would also be at risk.
Some Eagles have been known to take prey up to 4 times their own weight. While they are unable to fly away with prey this size, the will kill and eat it.
IMHO Pets under 15 pounds (7kg) should never be left out alone.