I would tend to think they hadn’t missed them, just wished they’d quietly go away. 
Another thing to realize is that the Supreme Court’s role has changed over its lifetime. Originally, the Supreme Court Justices “rode circuit”, actively trying cases and acting as more like the modern Courts of Appeal. In addition, a great deal of their appellate case load was appeals as of right, where they didn’t get to choose the cases they decided. Much of their earlier case law was on rather minor points, and not much cited or followed. Over time, the classes of cases where there can be an automatic appeal to the Supreme Court have been significantly reduced. Today they almost exclusively hear cases they decide to hear by issuing a “Writ of Certoriari”. As such, most every case from the last bunch of decades ago or so is considered significant and widely reviewed, but many from a century or more ago are little more than ignored squibs.
Further, until Erie Railroad v. Tompkins (1938) when there was a case in the federal courts based on diversity jurisdiction, the federal courts applied federal case law to decide them. Erie held that federal courts had to decide diversity cases based on the state law of the state where the case was brought, instead of under federal law. Pre-Erie, the Supreme Court decided many cases which set out the federal of many subjects that are today controlled by state law, and Erie essentially rendered all of those cases irrelevant.
Another change in the 1930s was the introduction of the Federal Rules of Civil Procedure (and other Federal Rules). This significantly changed the procedures followed in federal courts, and abolished many prior procedural matters that had been the subject of extensive litigation.
Because of these factors, along with the explosion of federal statutory law development from the New Deal to the present and the growing recognition that federal Constitutional rights control many factors in state criminal and civil litigation, the types of cases decided by the Supreme Court today are significantly different from those decided more than 70 years ago. As such, it is not uncommon to find pre-1930s cases where the Supreme Court ruled on matters potentially relevant to a current case, but because of context the ruling just isn’t particularly relevant. Although the Court’s interpretation of the U.S. Constitution and federal statutory law will likely be worthwhile to cite, something like a pre-Erie case on contract law will most likely be quite properly ignored. Also, in a common law system, there will always be outliers and abberational cases that get overlooked as case law develops in other directions, and courts recognize that a single older case going against a more modern trend isn’t worth much.
Accordingly, with the exception of a healthy number of landmark or widely-cited cases, it is not common to find controlling Supreme Court case law before World War II, and where an earlier case has not generated subsequent case law following it, courts will freqently give a judicial shrug and either ignore it or just cast it aside.
Is there more than one example of a Supreme Court ruling that explicitly stated it was *not * to be used as a precedent? What would be their decision if a case were brought before them that did so anyway?
Slight tangent: I understand that the Supreme Court can overturn a previous precedent with a subsequent ruling, but is it possible for the Court to revisit the original case itself? Let’s say that a decision had some sort of unintended consequence that needed a quick remedy – would the Court be able to amend or reverse their previous decision in that case, or would they have to wait for another case on the issue to percolate up to their level?
The only case I know of where they explicitly said that was a little electoral-dispute case called Bush v. Gore from… a few years ago. And if anyone later cited it as precedent, I assume they’d either primly remind the litigants that it was not to be cited as precedent, or ignore it entirely.
By “the original case,” do you mean from many decades earlier, as in the OP, or pretty recently? Unless there’s a “case or controversy” that requires them to revisit the original case, I don’t see how. If it’s recently, one party or the other, or the court itself sua sponte, could move to reconsider. Such motions are granted extremely rarely.
I can think of a few kinds of cases where that might happen, and I seem to recall reading about a famous case (whose name and facts I can’t remember just now) where a party got the court to reopen a case in order to reconsider an injunction or declaratory decree or somesuch. Cases involving interlocutory-type relief like injunctions are probably the best example. I wish I could remember the case I’m thinking of.