I think the idea is to make very minute changes that then become large distances in the bigger playground of space (and time). If you detonated a large nuke near an astroid and you observed it from close it would look like nothing changed. However, over a distance of one hundred million kilometers the vector will have changed sufficiently for it to now miss a small target such as Earth.
Once the "rocket" is in synchronized orbit with the mass that needs adjusting it should not need any management. That's the beauty of this. Once the mass is there the laws of the Universe play themselves out. No computer to break down and cause it to fail after the synchronization phase (which Murphy therefore states will be the time this does, indeed, fail). You are also going to need a substantial mass. Might be very costly to launch.
The problem here is that this requires early detection and some astroids have crept up on us and missed us by a hair (in space terms) before anyone knew they were there. Another geneal problem is the gravitational pull of Earth itself. Because it want's to attract the astroid ("Bad Earth! Naughty planet! Stop doing that!") you actually have a larger target than the width of the planet. You can imagine this as expanding the planet to adjust for its gravitation. Therefore, it would seem to be a weakness of this method as it needs to act over a long period of time as there must be an optimal point where changes in orbit are most significant. (well, duh, concentrating the work over 20 years into a one second blast would obviously be better..just stating the obvious here).
