i had a problem with my chickens. turned out to be a rabid coon that went into the coop and snapped their necks. dont underestimate their power, if they want in, theyre getting in! my dad saw one rip the top of a garbage can off that he crimped the lid down on and he could barely get it off, they got it off with ease. most likely it was a rat or a weasel or a coon. if theres a space big enough for it to stick its arm through, itll get whatever it wants, they have a very long reach. i would set up a trail camera if you have one, put it facing the cage with some chicken or lunch meat tied to a string on the side of the cage. that may satisfy whatevers getting in and spare your chickens. to get it, id do what justin said and set a rat trap but put it under the cage and bait it with chicken and some feathers. drill a hole through the bottom of the trap and wire it off to something un movable. that should catch whatever is getting in. if that doesnt work, use a cage trap and then you can do whatever you want with your varmint