Zombies are dead, they will not reproduce and have child zombies, and don't heal up all that well. They would have to continue decomposing at some rate, even if they are reanimated. In any real zombie infestation, out lasting them would be pretty easy if you have a good supply of food and water to last a couple of months and locked your doors.
In the original Night of the Living Dead, the main characters had to spend one night boarded up in a farmhouse. By the next morning, the remaining townspeople had rallied together, brought out weapons, and were on the attack, swiftly slicing through the undead like a hot knife through butter. A real infestation would be more like that.
Unless zombies were protected, as either wild animals, unaccountable people or a population control measure.
The New Endangered Species
http://tamarawilhite.hubpages.com/hub/The-New-Endangered-Species-a-short-story