The problem hasn't come and gone. This is the only time it has happened. And since hitting the reset button magically fixed it, I may not disbelieve some people's stories about the (lack of) reliability of Kenwood units.

I crimped the connections when I originally installed it, since I'm not exactly an expert with a soldering iron. They were all fine, and still are.

So, as it stands now, it's working fine, and I have all of my settings put back into the unit. If this sort of thing becomes a recurring problem, I'll be looking at ditching the head unit altogether and doing a proper amp install sooner than I had planned to. I don't use the radio or CD functions of the unit very often anway; it's more of an in-dash amplifier for me.