People like to think that predators all behave the way they read about in the books but they are not. They believe certain ones are nocturnal and always behave in certain ways. They don’t all follow that pattern. I’ve seen coyotes, bobcats, foxes, skunks, and others hunting in the middle of the day, I even saw a possum feeding from my compost at 1:00 pm on a sunny day and possum are supposed to be purely nocturnal. I did not expect to see that possum at that time. A neighbor saw a bobcat take her rooster in the middle of the day while she was looking out of the kitchen window washing the lunch dishes. Some of them are more nocturnal, but a lot of the time they are just really good at avoiding being seen. Human activity can keep them away too so nighttime is your highest time of danger but not your only time.
People think that certain predators always leave certain signs or go for specific body parts when they kill and eat. They don’t. There certainly are trends and most predators tend to follow those trends but all of them don’t always.
The only predator known to usually leave no sign is a human. Can you rule that out?
Coyote, bobcat, and fox are certainly on my list of possible culprits that could carry off a chicken and leave no trace. I’ll add dog to that list. I had a dog attack one time, two very large dogs that were abandoned in the country, where I lost eight chickens. I found one body, three piles of feathers, and no trace of the other chickens. If we knew where you are located we might be able to come up with more suspects. With the attacks being a few weeks apart I suspect it might be something that regularly hunts a large territory and makes a regular circuits or maybe a dog that is let out on a regular basis, maybe someone bringing a dog to a country house.
The only way to really protect your chickens is with barriers the animals can’t cross. I shoot and trap predators but all that does is remove one that is actively hunting your area. There can easily be more than one, I’ve often trapped raccoon on successive nights so more than one was visiting at the same time. Even if there is only one, there are plenty more being born. In my opinion removing one that is hunting your area is a good thing but that’s just a temporary or partial solution. It is not going to end the threat.
To remove it you need to know what it is. Different animals may require different trapping techniques or different sizes of traps or bait. It would be nice to know where to put it. To shoot it you would need to set up an ambush, these things can normally detect human motion really well and you generally don’t have time to go get a gun and come back when you spot it even if you could do that without frightening it off. Since your attacks are a few weeks apart how do you know when and where to set up an ambush?