Why does a battery stop working?

They don't. It's a chemical reaction. Which means that primary batteries ( like Duracell) convert stored chemical energy into electrical energy meaning flowing electrons. As you use a device, the electrons are used to power it. Over time, the chemicals in the battery have no more electrons to give and the battery "dies,"

Every kind of battery has its own history on how they stop producing electricity.

Basically, as the first answer stated, its a chemical reaction, but none of them stops the same way.

To read more about batteries, please see the Related Link below.