If traffic to a Skyhook is "unbalanced" (more mass going in one direction than the other) the orbit will change. You can make it up over time with electric propulsion. Since electric propulsion is at least ten time more efficient than rocket fuel, you still come out ahead.

In Earth orbit you can potentially react against the magnetic field by running a current through the ionosphere. That uses almost no fuels, just a little gas to make plasma contact.