I've lifted this this post in its entirety from another forum:
Food for thought if any of you have a number of deer on your rough shoots. Over the past couple of years the woodlarks in the Brecks have been suffering very heavy losses in the nesting and fledgling stages. A team from the University of East Anglia set up a number of CCTV cameras over woodlark nests thinking the main culprits would be crows or foxes. 1 nest was taken by a crow . 1 by a badger , but 12 were taken by muntjac and roe deer. Not only were the eggs taken the deer also eat young fledgelings out of the nests. This may not be as far fetched as it sounds as I seem to remember hearing years ago of sheep that were taking sea bird eggs in the western isles.
I have little doubt that if the deer will take woodlark eggs they will also take gamebird and duck eggs so it your predator culling this spring did not seem to work perhaps you need to look at unsuspected egg predators