Still puzzled about why power cycling would improve things, but of course I'm no EE! :-)
Along the lines of my earlier comment, being an EE and an experienced digital and analog circuit designer, as I am, won't reduce the puzzlement :-). At least without having highly detailed familiarity with the specifics of the design.
With complex digital circuits, and particularly when software and/or firmware programs are also involved, puzzling and counter-intuitive phenomena are almost to be expected at times. And keep in mind that modern digital circuits are far more complex than they may physically appear to be, since some kinds of physically small integrated circuit devices commonly contain many millions of transistors each.
Could there be any connection between the beneficial effects of power cycling and the fact that, when the unit is powered down, it often emits a broadband pop/thump? Could there be some kind of "buildup," the elimination of which results in better sound?
My quick initial instinct is to say no, and to consider the thump to simply reflect a turn-off transient that would have no associated or secondary effects. And to expect that what is somehow responsible for the improvement you have observed is either the reset that occurs when power is turned on, or resetting or clearing that occurs by virtue of circuit devices being unpowered. But then again, who knows?
All the best for the holidays and 2012!