I doubt you're going to ever find a definitive and specific date. But you can bet that 1989 was the beginning of the end for the small-ish bicycle market that Japan was exporting in the first place (and Japan was exporting A LOT of goods...which was another factor that some in the USA did not like). Just too many factors going against them during that time period. Again...there is so much to digest during that era that finding the "why" is going to be much easier than finding the "when".
I'm not sure why you're that concerned with the "when" though. The "why" is vastly more interesting and makes timelines pretty easy to extrapolate out. If anything, I give Japanese bicycle manufacturers credit for being smart enough to see what was going on and peek into the future and know that a certain way would not be sustainable (I don't like it, but I get it). Even a lot of US bike manufacturers only held out for so much longer. When was the last time Trek actually made a lugged bicycle? Now they're in financial trouble for making "too much"...and none of what they made "too much" of appeals to the C&V in me.
Trek last made a lugged bike in '93 with the 520 touring, and a regular road bike in '92 with the 400.
And that's what the thread is about. You are welcome to start a why thread. I started this thread because I am genuinely curious what might have slipped through for a few years more that no one is thinking about.
This thread is also about Taiwan, and that story doesn't have as many whys.