The magnet analogy works here, so let's give it a try. Put one magnet on a table and then put one under the table so that it's held up by the magnet above it. Then observe what happens. This will take a while, so maybe go get a 2^128 cups of coffee.
The space between the magnets is expanding, just like space everywhere. Assuming the table and magnets are immune to deterioration over time, you can come back after several billion years and the distance between the magnets will have stayed the same. Space expanded, sure, but the stuff occupying the space didn't.
The forces that hold an atom together are significantly stronger than what's holding the two magnets in the example above.
