Sounds like maybe a racoon or possom. OR maybe a fishercat if you have them where you are.

Are they free-range?

Yup, I'd set a couple traps & ensure the safety of the last duck.

Thanks for the reply. They were out during the day and put away when it got dark. (we just got home a little later Thursday) The small opening that they were pulled through, makes me think small. Yet the one that was completely gone makes me think bigger. My son told me he saw what looked like a Fisher when he was scouting the area a while back. After 3 nights of traps, I have nothing.

Put some kind of bait inside your trap...like a raw chicken breast.
A gal in Maine on another board has been having problems too. They have caught 2 coons. The description of what happened is very close to yours. If you start missing only one at a time...watch for hawks. She had that happening during the day also!...a golden hawk!

I just wanted to give an update / conclusion. My wife caught the perp red handed (a Mink) but it got away. It had got to our last duck by chewing / digging a hole through the wall of the chicken coop. (Which was plywood, insulation and panneling) To catch it, I baited the trap with what was left of the last duck and had him within 2 hours. I can't believe that little Mink went through a half dozen ducks in 3-4 days. My wife is scared away from starting over with new ducks. She says it's because we can't keep them safe.

Well I'm glad you know what it was, and Im sorry about your last duck.

A ferret can get through a 1x2 opening, being minks are relatives I suspect the same for them. Why not line your chicken coup with hardwirecloth? Top, bottom, sides. Those 1/2 x 1/2 holes nothing is going go get into, unless it's a bear or something.
Our coop door is a 2x4 wooden frame screwed together, with cross braces, and lined with hardwire cloth. It has withstood over 15 years and still going strong. The rest of the coop is concrete floor and walls, then built like a house. Nothing short of a bear is getting in there.

Brendasue

Thanks Brendasue, I also appreciate the tips on fortfication of the coop. I figured if it would chew through the plywood wall, what would stop 'em. We have some of that wire mesh so maybe I'll talk her into more ducks. We really enjoyed the eggs.