I figured out the answer this afternoon--I like to do this, find the exact (often very late in career) moment a lifelong .300 batter's BA slipped finally and irrevocably under the .300 mark. I did this for Keith Hernandez, and Mickey Mantle, and it's a bit tedious, searching for the month, the week, the game, the at-bat that a BA went from .2995787485 (say) to .2994801049. Anyone care to guess before I show my work? For all I remember, this was a major news story, and lots of people know when it happened, but I can tell you that with Mantle, not only did no media source note the moment, but the NYTIMES didn't even carry the box score for that game.