Would it be possible, using current technology and renewable energy sources only (e.g. photovoltaics), to magnetically polarize external shields of orbiting satellites in such a way, to effectively prevent or substantially delay orbital decay, or to perform micro adjustments to their orbits (vertical only), by pushing or leaning against Earth's own magnetic field? Which considerations need accounting for, have such mechanics been proposed before, or even already in use? If not, how does Earth's magnetic field affect magnetically neutral and inert artificial satellites and their orbits?
NTRS to the rescue:
Alternating Magnetic Field Forces for Satellite Formation Flying (2012)
Youngquist, Robert C.; Nurge, Mark A.; Starr, Stanley O.
Selected future space missions, such as large aperture telescopes and multi-component interferometers, will require the precise positioning of a number of isolated satellites, yet many of the suggested approaches for providing satellites positioning forces have serious limitations. In this paper we propose a new approach, capable of providing both position and orientation forces, that resolves or alleviates many of these problems. We show that by using alternating fields and currents that finely-controlled forces can be induced on the satellites, which can be individually selected through frequency allocation. We also show, through analysis and experiment, that near field operation is feasible and can provide sufficient force and the necessary degrees of freedom to accurately position and orient small satellites relative to one another. In particular, the case of a telescope with a large number of free mirrors is developed to provide an example of the concept. We also discuss the far field extension of this concept.
EDIT (thanks and a tip hat go to Tildal Wave, the author of the original question):
This design solution has gotten a Wiki page all on its own: Electromagnetic Formation Flight
It doesn't make use of Earth's magnetic field, though (one would have to pull multiTesla magnets into orbit for that), so a notice to upvoters: please keep in mind that this answer doesn't seem to match the question fully.
I think a better answer would contain calculations on the heights and inclinations where using Earth's own field is feasible for a given intensity of the spacecraft's magnet (that is, average altitude gain during a month of operation through magnet manipulation exceeds altitude loss due to atmospheric drag).
Necessary parameters/data for calculations: full Earth's magnetic field model, solar activity index (to account for drag and magnetic field variations), craft's ballistic coefficient, magnet size, orbital inclination. Basically, one has to derive optimal control law for the magnet, and apply it along a fixed period of time.
There's been a recent article (http://dx.doi.org/10.2514/1.57479) called "Orbit Boosting Maneuvers for Two-Craft Coulomb Formations" in the Journal of Guidance, Control, and Dynamics.