I haven't lost any but, thanks to a plethora of feral cats in the neighborhood, I built my cage with predators in mind. My girls aren't allowed to free-range because there's too much of a chance they'd hop the fence, land in a neighbor's yard and get killed by a cat or dog before I could get to them.
I'm using an old dog kennel for their enclosure. It's actually attached to the wall of my back porch (really convenient because I built the nesting boxes INSIDE the porch and just put one open end into their coop. I can step out on the porch, open the cupboard doors on the nesting boxes and retrieve the eggs without having to deal with inclement weather!). The dogs had pulled up some of the chain link so I went around the inside of the kennel with chicken wire and topped it with the plastic chicken fence. The floor is dirt-covered concrete.
I suppose a truly persistent predator could chew through the top pretty easily but it would be one very intelligent predator to think of climbing up to the top to begin with, he'd have to drop into the pen from above and would then likely be trapped. And he'd have to do all this very quietly, even at night, since my bedroom is only about 8" from the pen.
Along with the cats, we've had a skunk around almost every night all Summer long (my idiot dog got "skunked" twice in August - I'm so glad I keep a bottle of Nature's Miracle on hand!!), one of the neighbor's dogs keeps getting loose and I came home in the middle of the night one night to see a HUGE Opossum in the driveway (I've NEVER seen an opossum here in the North East and I'll bet this one would weigh in at 8 lbs MINIMUM. It was standing beside my daughter's Subaru Outback and was half the height of her tire!). I've got to think it was drawn here by the chickens. I inspect the cage on a regular basis and haven't seen anywhere that shows signs of anything trying to get in.
My own dog, a Pit/Springer Spaniel mix, is terribly curious about the chickens. Once they'd gotten a bit of size to them, I let Charm follow me into the pen one day. She sniffed everything in sight and attempted to sniff one of the girls who immediately flapped her wings and tried to rake Charm's face with her claws, lol. Charm couldn't figure out what the chicken's problem was, lol, all she wanted was a sniff! (Charm's plenty fast enough that if she'd wanted a taste of the chicken, the chicken wouldn't have had a chance. She WILL chase cats or other dogs off our property that don't belong here - which is how she got skunked - but will not chase anything that belongs here. If she were to get loose and someone else nearby had chickens, I make no claim that she wouldn't eat THOSE chickens, only that she shows no inclination to eat MINE.)
Overall, I've been very lucky with my first ever chicken flock! As the weather cools, though, I may have to reinforce some parts of it against rats as they start looking for warm places to be and things to eat.