Two theories on this subject to which I completely subscribe, although I have no concrete evidence of (though not for a lack of trying) and are based on years of experience/observations, are that (1) in the last minute or so of a game the losing team's likelihood of making 3pt shots is increased, and (2) the corrective measure which kicks in after a certain # or % of shots have been missed is either too significant or the threshold which triggers it is too low.
#1 - The only evidence I can offer for this theory is that whether my team plays a man or zone defense I set them to the most extreme perimeter defensive setting for the last minute of the game if my team is winning by 3 or more points. From almost the very beginning I've done this because even early on I thought this was out of whack, and for several years I even kept detailed notes on a game-by-game basis concerning 3pt% of opponents in this scenario. And would compare these numbers against overall averages in every way imaginable. However, because its hard to find any data to really compare them with since nobody either plays or faces a +5 defense on a consistent basis, I eventually realized it wasn't an endeavor that would yield any REAL proof. Despite this, it did serve to confirm my initial and personal suspicions. This is because, whether playing a man or 3-2 zone at +5 in the last minute of a game when winning by 3 or more, although the completion percentage decreased it did not do so in any significant way. If I was forced to give a general quantification of these numbers, then the easiest way to frame it would be something like this: normally opposing teams were only 25% less likely to make a 3pt shot in this situation. From what I recall, teams which had a number in the 35% range were definitely on one extreme of the bell-curve. Also, very often when I'd adjust these individual season numbers to reflect only those games against quality human coaches or great sim teams (which is almost always still more than half my games every season), I found this number significantly increased to around only a 15% reduction in likelihood.
#2 - Admittedly, I have much less observable examples for this (though again, not for a lack of trying), and at worst someone could argue this is circumstantial - to which I wouldn't have a great defense. There was actually a recent good discussion of why sims with terrible PER ratings (let alone others that go into perimeter scoring) can still shoot around 25% or so from behind the arc on the season, and I think it hit the nail on the head for the most part but stopped just short of my position on the issue, which is that I think this is more often than not due to the fact that these teams also take a very large number of 3pt attempts. Which (although they probably disagree with my opinion here) is latently expressed by other coaches in this thread because I too almost always go +2 or +3 against sims teams based purely on the number of 3s they take - no matter any of the other factors involved. The other thing which plays into this factor, and this is the point where I put on my tin-foil hat, is that I think this is the most recognizable with individual player performance. Nothing shaped my view on this more than the difference it makes between setting a players 3pt frequency from -1 to 0, specifically in that players with average PER ratings actually performed better from behind the arc. Most surprisingly, I noticed that it not only increased their 3pt% on the season but also decreased variance on a game to game basis. For the sake of brevity I'll put it like this, it use to be common for a guy on my team to go 0-2 in a game, now it is just as common (if not more so) to see a guy go 1-3 from behind the line, and in those rare occasions there is an 0-3 it is almost always because they took a half-court shot.