Looking at the link that Tom Servo posted, it seems that the Brady's began crashing and burning between 2000 and 2002. While it's unfortunate that it took such an event, I really think that 9/11 was probably the turning point. The reason, I think, is two-fold. First and foremost, I think that event served as something of a wake-up call for many and made them realize that, despite any gun control measure, we simply cannot legislate our way to safety and security. Suddenly, the worry-free little bubble was burst and owning and carrying a gun became a very comforting thing in a scary and uncertain world.
Likewise, national security and foreign policy jumped way up on the list of most people's priorities and thus gun control saw its face time drastically reduced. It seems that after 9/11, many of the driving politicians behind the gun control movement suddenly found themselves with other, more pressing matters as their constituents became more worried about the other aforementioned issues.
Smith, and Wesson, and Me. -H. Callahan
Well waddaya know, one buwwet weft! -E. Fudd
All bad precedents begin as justifiable measures. -J. Caesar