Say a disc is oscillating without slipping in a circle about its stable equilibrium. I've thought of it this way:
I assumed a disc is placed at, say, 3 degrees from the equilibrium. The rotation starts and since there is slipping at the surface, dynamic friction acts and makes gets to the no-slip condition by rotating the disc about an axis from COM, but there still has to be static friction after this to make sure the accelerations at the surface should be same such that no further slipping occurs.
I understand the fact that when dynamic friction acts there is a loss in energy and the disc won't go back to 3 degrees but when I calculate the static friction I end up with a conservative force and conclude that after the initial loss static friction acts as a conservative force.