You would be surprised what ONE vermin can do with a bit of time unobserved. Our number one thief around here are the weka (a native bird) - One morning I observed ONE bird making repeat trips into my hen house to steal eggs and in the space of 30 minutes it took 8 eggs.
It was a bit of a coincidence.. but several days prior this weka had got itself into my wild cat trap (which is a live catch trap). Weka are protected birds here so I duly released it, but not before putting a coloured leg band on it for easy identification later.
I had also been experiencing egg reduction at the time and I wondered if this weka might be the culprit so I laid a trap. I "doctored" several eggs by injecting them with a whatever I could find at the time that I decided would taste bad - the idea being to dissuade the thief from even wanting to take the eggs.
And it was the leg band gave it away! The same bird.. repeated trips until it stole nearly all the eggs.