Get a game camera and if you might want to get a driveway alarm and set it up at the gate to that pen if you have one. The alarm will chime if someone drives or walks up to the gate. I think people are stealing your goats.
I would vote for coyotes. We have problems with them around here, and everyone has dogs. They even take dogs. Baby goats would be just what they would take.
Sounds like the ever stealthy cougar. Here's my experience with live stock and lions. When I was kid I lived on my uncles farm for a while in Oregon. He had many goats, sheep, some cows, and other critters. A local lion killed/ harvested all the goats and sheep, about 14 total in about 5 years. We knew it was a lion because my cousin and I ran in to it and spoiled it's huntone night. We had worked on the farm all day. At dusk my uncle came to pick us and take us home. Just after dark the goats started calling loudly. So my uncle gave me and my cousin two flashlights and off we went to see what all the comotion was about. We walked about 40 yards from the old homestead to where the first nubian buck was. He was chained to a huge mature standard apple tree (full size), not like the semi-dwarf ones you usually get today. The buck had pulled his chain as far away from the tree as it could get. He just looked at us like what are you doing here? We were puzzled about why he was acting so oddly. We were about to bypass his spot and go onto to check the other chained goats when something caught my eye. I paused and told my cousin to shine his light up in the tree above us. Something shined a little from the edge of our lit area in the tree above. When we did, I about spung a leak in my pants. just above the buck was a full grown mountain lion perched on a large branch. the big cat snarled and hissed at us. Then it jumped down ran one way and we went in the opposite direction as fast as we could. It was a cool experience, but frightening at the samre time. My uncle was an accomplshed outdoorsman. He tried many different techniques to get that critter. He never did catch it. If you do have a lion taking your animals, good luck catching it. Hunting dogs and horses are about the only reliable way to do it.
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My part of texas has not had lions in FOREVER.. the closest wild lions in my area are at least 90 miles away... I know its a possiblity... but if it were a lion... why just babies.. its like us eatting meatballs when we can have a hamburger...
According to the "experts", the only mountain lions left in the US are in Florida. Of course, those experts dismiss sightings and documented encounters with cubs in several states over the last few years.
Somebody should tell those experts where baby mountain lions come from.
I may be in the minority, but I vote Coyote. The fact that they are after kids and adult goats makes me think four-legged predator. I had a terrible time with them getting goat kids until I upgraded all my fences. But with property the size of yours, I don't know what you would do besides get LGDs to stay there 24/7.