I discovered an unexpected egg thief just last week.
I was running late for an appointment, so let the ducks out of their house and threw out some food. I saw there was about 4 - 5 eggs in the house, but figured I could get them once I got back a couple hours later. When I did get back, the eggs were gone, shells and all.
A little more looking around the yard and I discovered two empty, cracked egg shells in the citrus grove next to my property about 40' from the duck house the eggs were laid in. I noticed a footprint in the sand of the grove indicating 'coon or possum.
The next day, I released the ducks, threw out some feed, and pulled up a chair a little distance away and waited. No possum, no raccoon.
It was the CROWS!
I watched as a trio of crow flew in to peck at some leftover duck food, then meander into the duck house. They pecked and ate at the eggs until they were empty. Once cracked and empty, they would grab the shell and fly away with it. This also explained why it appeared the ducks were laying more eggs on the weekend. During the week, I gather the eggs before work, around 6:00am. On the weekend it's closer to 8am. I suspect that during the week, I was getting the "early" eggs and any eggs laid after I left for work were being "stolen".
My first solution is to make the morning duck routine the absolute last thing I do before heading to work, so far it seems to be working as I gather 3 -4 eggs consistently each morning from my little flock. The other solution is to cull the crow population some more. I'm told crow and other wild animals will recognize "dangerous" areas and avoid them although I'm not sure how true that is.
Good Luck,
Rich