Your pop constantly increases, so it takes more and more food to feed. So the expected time when you'll run out of food keeps decreasing a bit because consumption increases.
Also, there are diminishing returns on distributing resources in the game. If you distribute 10,000 food units they might last for one day, but 20,000 will then last for a less than 2 days, and so on, because the game makes more of them go to waste if you distribute a lot. So you should distribute as often as possible.