Question

Why do the outer stars in our galaxy not slow down, as Kepler’s laws of motion would predict?

Answer 1

Kepler's Laws were derived for the planets orbiting the Sun in our solar system. And they work for any situation in which you have one discrete object with a mass far greater than any of the the objects that orbit it. But with galaxies you have a very different situation. The mass of a galaxy is not all concentrated at the center. It's spread out among all the constituents of the galaxy, across hundreds of thousands of light years. As explained here, even the supermassive black hole at the center of the Milky Way isn't massive enough to greatly affect the orbits of the stars in our galaxy (except for those very close to the center).

In practice, and this is especially true for galaxies' stars, the paths are not perfect ellipses. There is often some precession (a slow change in position) of the orbiting object's path, causing it to never repeat the exact same orbit about the central mass.