WE had this problem too....and no broken shells....then my daughters caught a snake that my cats found and were checking out. his loud HISS is what we heard.
Now, we are finding broken eggs, and i think that is actually a racoon or opossum or skunk, they are abundant in our area and we have caught in the past several of each....an opossum family found a way into a dresser in our garage!top drawer!!!
The only eggs that have been safe are in the coop...we scooped up several and placed them under a broody chicken and they hatched! all but one baby duck is in the house, and the chicken turns out to be such a good mommy! we pull out baby, then put her down and Midnight (a speckled sussex, don't ask) shoves her back under very gently.
I have tried to get my ducks to go in at night and I finally quit. They had me running back and forth every night. Forget it! the chickens are all smarter than them. (except the broody one in the tall grass that we swapped infertile chicken eggs for fertile duck eggs...)