The farm has crop cycles just like a real farm, and it supplies a certain amount of food with each crop. The frequency of the crops is determined by your game speed setting. If you have a lot of villagers (more than 15 or so, including babies and children), the amount of food you get from each crop may not be enough to keep the food supply stable between crops. Even if the food in the bin is depleted, your villagers will not die immediately, though. You might want to start having them work at the research table whenever the farm is empty so that you'll gain enough points to purchase the final level of harvesting, since only the farm and the berry bush are available at your current level. They won't gain as much farming experience if you do that, but your villagers will be able to go fishing sooner, and food will no longer be a problem.