First, have you used a fence tester to check the voltage all around your fence? Also, what kind of charger are you using? Second, Opinionated Opinion coming up here, in my decades of experience with electric fencing I have found that you want a fence charger from West Virginia Fence company in Lindside WV, nowhere else. There's no comparison on the strength of the charger from any other source, no matter what voltage they claim. WV solar chargers , with one of their nets, is used up north around beehives to keep bears out of the hives. Yes bears, and yes it is successful. So if dogs got through your fence, there's something wrong there.
When I had my big farm I had sheep, chickens and turkeys free ranging. I also had a female English Mastiff living with them. Never lost anything and the dog was totally trustworthy even with lambing ewes and newborn lambs, blood and birth fluids etc. That was a dog-eating, coyote-eating dog, and big enough to handle pretty much anything. Also perfectly safe if the neighbor's toddler got inside the fence, the toddler would just be added to what should be protected. The downside on the mastiffs is
1. giant breeds don't live too long, 10 years is a long life
2. breeders don't want to sell you a dog for working, they only want to sell to people who will show
3. cost. You really have to hunt around to find a non-show dog, as in less than $1500
4. probably not an issue with a poultry operation, but mastiffs are short coated and need shelter (like in a barn cuddled up with warm sheep) in winter
5. be very picky about where you buy from, many lines of giant breeds have multiple genetic problems like shoulder dysplasia
I currently have a Maremma livestock dog with my chickens, pasture is fenced 5 feet high with 2x4 inch welded wire, one electric tape at waist height and one up on top of posts about 6-7 feet because I need a deer deterrent also. Nothing, I mean nothing, is coming in here with that dog. He is only 80 lbs. and there are no show Maremmas, so there aren't the genetic health problems. He's long coated, won't use any shelter even in below zero. The downsides?
1. the puppies have to be trained not to "play" with poultry. Sheep and large animals don't seem to be a problem, but ducks running away triggers a chase response. The best way to do this is with a hunting dog electric shock collar, which some people think inhumane (no, it's not)
2. they seem to take a long time to mature from puppy mentality to adult responsibility, I'd say absolute minimum 1 year and closer to 2 years, compared to the mastiff, who was working before a full year old. Of course, the Maremma lives longer too.
3. they are specialty working dogs and expensive, mine was cheap at $750
4. they are working dogs only, NOT suitable as house pets or in small yards. If they don't have a territory to patrol and protect they can get very weird. For this reason breeders won't sell you one if you haven't either got acreage/farm, or have experience with livestock dogs. I only have 3 and a half fenced acres and that is pushing it with one of these guys.
Other dogs are possible, be aware that Great Pyrenees often deter predators by continuous barking, like all night, (Maremma only barks if there's something out there) and can bother you or upset the neighbors. You can often find crossbreds of various livestock breeds for around $200 for a pup, Anatolian, Maremma, Pyr, etc mixes . in local farm newspapers.
But your own livestock protection dog is the way to go. I've never lost a bird, never lost a sheep, in an area where beef cattle calves were killed by coyotes, and there were no stray cats because they were all eaten. Good luck!