It is caused by the fact that a year is really 365.25 days long or so.
I say, rather than just having another day every 4 years, we should embrace it's not-there-ishness fully and just go for a total imposition of anarchy for 24 hours, time to settle scores and make those power plays, kill the ex wife (or whoever) or even just strip her skin off and pour acid on her for a few hours, and all of this would be legal on National Non -Day. The laws , rules, regulations and other nonsensical bullshit could be left aside for one 24 hour period.
Anarchy you say? What the fuck is my problem, eh? Well it seems to me that although I am proposing total disolution of order in American society for a short period every 4 years, it is the nature of true anarchy to cause the development of "government from within". It is my observations of human nature that show me that only those with no self control will find themselves out of control on NND. And a squeeky wheel will get greased.
All this having been said, I do think that this should only apply properly to the non-military population, which indeed would include the police, and since those police and their antagonists would suddenly be unbound by the normal rules of engagement, it would likely be a very colorful day in America.
Further, upon the end of NND, the military would likely, for the first few occasions, be called upon to stomp the piss out of anyone that doesn't quite get the idea that all good things must come to an end.
As far as liability goes, there would be none at all, criminally speaking, as long as there was no ongoing torture or infliction of physical pain beyond the termination of NND. And as far as civil liability of course any suit brought forth claiming a cause of action based on events occuring within the timeframe of NND would be required to be summarily dismissed with prejudice. Of course, there would be a simple need to protect ones property and loved ones for......