Hi Carlos,
Yes, granaries, roads and groceries crumble after some time. The exact lifespan depends on the type of building. It is also directly related to the quantity of food you spend playing. If you only play Lost Cities, a granary will last for something like 150 games if I am not mistaken. But it is a bit more complicated than that. They last longer when you have many granaries so that the actual benefit of each extra granary is about the same as previous ones.
Granaries are in any case a better option than buying food directly from the market.
Finally, as buildings age with food eaten, they don't age when you don't play. And also, if you have magic potion, buildings do not age at all (as you don't need them).