The bug

If villagers pick up wheat in different mounts in separate stacks, even though they have enough wheat to craft bread, they don't realize that.
This causes villagers to fill up their inventory, making them unable to keep collect anymore crops, and since its inventory can fill up of non food items (wheat), at some point villagers wont be able to reproduce.

How to reproduce

1. Summon villager
2. Throw him 2 wheat in a single stack. Wait until it picks up the bread.
3. Throw him 1 wheat in another stack
4. Do /data and take a look at the inventory tag

Notice that two different slots have wheat inside them, one with 2, and the other with 1.

This happens since 1.14.

Update: As pointed out by Pelle Reinke, it no longer happens with farmer villagers but any but them. Reproduction steps might have been changed since this steps where provided.