First of all, eggs are generally much more robust than commonly thought. Food safety advices for eggs vary a lot, but healthy (chicken) eggs can stay good for many months. If the eggs are contaminated with bacteria when laid or during processing, they can of course spoil or rot before their "best before" date as well. I didn't find any publications, but in this interview, a researcher from Nofima (a Norwegian food research institute) tells that they were not able to find any harmful bacteria in 7 months old eggs and even after 12 months, eggs are usually edible.
Back to the difference between chicken and duck eggs ... Chicken eggs are good for at least three weeks even without refrigeration. The reason for this is that the eggs contain natural preservatives, which are required for the egg to stay good during the nesting period. The natural purpose of the egg is of course to provide nutrition to the contained chicken, and it would probably not do the chicken any good, if it has to stay with a rotten egg yolk for several weeks. It varies between different duck species, but ducks generally breed their eggs much longer than hens. I am now just assuming, but I suppose that duck eggs have a similar natural protection as well, to keep them good throughout the longer breeding period and that may explain the longer recommended shelf life for duck eggs.