What happened, simply put, was that violent crime went up significantly. There is a chart here that shows the increase in violent crime, which somewhat closely tracks support for the death penalty.

This correlation has long been noted. Additionally, as that article lays out, there is reason to believe most folks have a very emotional approach to the death penalty, rather than a rational one. Therefore they hear crime is up, and want harsher punishment for it.

This more recent paper essentially confirms that the violent crime rate truly is a big factor, or at least people’s perceptions of it. It’s also a matter of discourse, of course, which is why age and cohort effects can have different effects. One generation might view higher violent crime as a reason to abolish the death penalty and undertake different forms of change to policy, in theory, like rehabilitative measures. But the default has typically been that more crime means more support for death penalty policies. And as this paper notes, public opinion changed also when crime became a national issue, as in elections starting in the 1960s. It’s also worth mentioning that race is a big divide in support for the death penalty, with white Americans favoring it significantly more. This may have played into the changes as well, depending on significant racial tensions at various points, but it also does not correlate with the changes themselves as much. It may have altered the peak in the 1990s after racial tensions rose during things like the Rodney King trial and riots, or OJ Simpson trial, or as desegregation continued, but I haven’t seen much of that in the research. You can read more about the disparity here, where it also notes by the way that support seems to have dropped by 2000, likely as DNA began to show of wrongful convictions and death penalty punishments that were carried out, shifting views on its efficacy and fairness.