Sorry for your losses. The only predator up here in Cent. MO. that can set off a live trap and back out are adult Red Fox. I know they will sometimes behead birds (neighbor shot one with nothing but a duck head in its mouth - left the rest of the ducks dead and wounded near their pond).
However, the last big fox attack at their place resulted from a pair of foxes that carried off all (13) of their Silver Laced Wyandottes in the space of 15 minutes. I found the piles of feathers arranged around the base of a cedar an acre north of their place along our fence line. She had just let them out and was getting them treats. If she hadn't walked back out when she did and saw the foxes heading off she would've never known what happened to her poor pullets (no feathers in the yard - no signs of struggle).
Since then, between our neighbors and ourselves, we've harvested six adults and destroyed two active dens.
That it is not carrying off the kill makes me suspect coon, but I've taken over 300 in havaharts over the past ten years without a backout (smart ones will try to push the trap over).
Is there any way you can lock up your survivors during the night? Whatever it is, it's not going to give up until there's nothing left to eat or it is retired from the target pool.
Take care,
John