How to reproduce:
1. Open attached project.
2. Compare created both GameObject Animations:
One cube has a particle system which is not animated.
Another has one which has the emission flag animated to true.
3. Open Animation for cube named "Not Working Distance...".
4. Create moving animation for cube to change its position.
5. Play the scene.
6. Notice that particle system with an animation on particle system component is not emitting particles.