The tiny pieces of shrapnel are slowly working their way into Tony's heart. So a magnet is placed to keep them out. This would indicate that the shrapnel is in fact magnetic (since the magnet affects it), so wouldn't a stronger magnet reverse the direction of the shrapnel's movement and cure Tony?
Since it is an electromagnet, wouldn't replacing the car batter with the arc reactor provide a significantly greater power source, thus improving the magnet's effectiveness, and reversing the movement of the shrapnel? Even if the original magnet was only slowing the shrapnel, the new power supply should have significantly improved the performance.
This is indicated by the fact he enters cardiac arrest when the arc reactor is removed, but recovers when it is replaced. Thus when it is removed, the shrapnel resumes it journey (at a very fast pace) into his heart, where it causes him to suffer cardiac arrest. If replacing the arc reactor simple causes the shrapnel to stop moving, then he would remain in cardiac arrest (the shrapnel already in place), but simply not get worse. Since the shrapnel is assumed to be removed from the position it was causing cardiac arrest, it should be assumed that the magnet is removing the shrapnel.
Basic physics says that if the magnet is able to move the shrapnel at all, the closer it gets to the magnet, the stronger the effect if the magnet, thus the more it would move it. So if the magnet is able to pull the shrapnel just enough out of the heart to recover from heart attack, then it would continue to accelerate away from his heart unless it encountered something to slow it down like a much thicker tissue (bone maybe?)