Great questions. I think the Reagan Democrats started to desert in the short recession of 1991-2 and as the culture war died away more of them left. Pretty remarkable that with someone so symbolically on the wrong side of the culture wars as Bill Clinton running, conservatives couldn't make more of moral and social issues, so there's some factor I don't see. Maybe the country was tired of eternal conflict, or maybe economic opportunities interested Americans more. Maybe we recognized that we have more in common with each other, or maybe we recognized that the big social changes had already happened and got used to some of them.
The other thing is that a lot of Reagan Democrats probably did go over to the GOP permanently. Today's Democratic base is very different in terms of sex, generation, race, region and profession from what it was in 1940, 1960 or 1980. They've made up for the loss of older, middle class white men with minorities, a younger generation, the more affluent, and, especially women.
I suspect most conservatives are pretty clear on what they want from politics. But many Americans today aren't very much like those voters of past years who only thought about politics once every four years. We are more like New Yorkers with a dozen parties on the ballot than old time Middle American straight ticket voters. We have all manner of media to agitate us and get us to think about the big picture. It's a characteristic of a rich country with affluence and many media outlets. So we're not just looking at the picture of what a President or Congress can realistically do in 2 or 4 years. We're looking at the big picture of what we'd ideally want the country and its governing philosophy to be, rather than about the questions that any President or Congress is likely to resolve.
The Reagan Democrats DID start to desert in the short recession, but I think it's much more complicated than the culture war dying away. Ten years of unremitting propaganda against the Reagan Revolution, combined with the fall of the Soviet Union had a tremendous effect. Combined with Bush's tax increase (and signing of such monstrosities as the ADA), the effect was to demoralize Reagan conservatives. The RD's no longer had an anti-communist issue and, frankly, Bush had killed the conservative movement, so they left. Had it not been for Clinton, it would still be in extremis. Perversely, Clinton was responsible for the reinvigoration of the Republican party (and, at least temporarily, for the ascendancy of conservatism).