I am not suggesting the Court reconsider every case. I am not even suggesting they reconsider any one case. However, if the Court gets a case in its docket, rather than simply looking for old cases, and seeing how other Courts ruled, why not (warning: Revolutionary Idea) examine that case on its own Constitutional merit, and rule accordingly? Following precedent is ok, if the precedent is sound to begin with. Otherwise, it simply compounds prior errors.
The Framers, our Founding Fathers, meant the Constitution to stand the test of time, or as you say so well, last for centuries. However, when it gets constantly re-written, based on the agenda of nine un-elected people, who have lifetime appointments, and who consider themselves the Last Word, then our Constitution starts to lose that ability to outlive each and every one of us. I would rather have Justices who read the Constitution looking for the Founding Fathers' original intent, instead of the modern meaning.
But the Founders dit not intend for a constitution that had to be amended every 5 years either. That is why they used broad language in most of the constitution. And that is why it is so important to look at the spirit of the constitution, rather than only at the word.
Of course the court should only follow precedent when the precedent is correct. But when you don't look at the reasoning of the court and only conclude that the precedent is wrong because the original intent was different, it could lead you down very wrong paths. For example, the Fourteenth Amendment was not directly intended to prohibit segregation or anti-miscegenation laws. However, the Supreme Court strook both down, looking at the spirit of the amendment and the constitution. I wonder what Thomas and Scalia would do in such a case. Were Brown and Loving wrongly decided?