Law of the Case or Judges Like to Only Rule Once

There you are, reading a case and some point of doctrine is utterly weird is in it, or as you're reading there's some really obvious argument comes to your mind that would blow one of the sides away, but it appears to be ignored by everybody. Now sometimes a judge will get fixated on a strange idea (Wyoming Supreme Court Justice Fred H. Blume's application of Justinian's Institutes and two of the Novels to Wyoming appeals comes to mind.) and sometimes all the lawyers and appellate judges in a room get caught up in groupthink, but more commonly these come up because some argument is foreclosed by the doctrine of the law of the case.
Look at a trial. In a trial, there is hardly any error that does not have to be preserved by an objection, etc. in order for an appellate court to consider that error. Therefore, in a trial, if there is not an objection, etc., no error can be successfully presented on appeal. Furthermore, whatever trial error that is not raised on the first appeal, can generally never be raised again.
Let's check out a successful appeal to an intermediate court of appeal (not a government's highest court) that results in a remand to a trial court. For this hypothetical, the intermediate court of appeal sustained two of three assigned errors and overruled the other. As to anything that was not objected to, etc. that error is waived, and any of those things which might be error has become the law of the case. Any preserved error that was not brought to the attention of the intermediate appellate court, that error is waived, too, and legal doctrines implicit in the possible erroneous rulings of the trial court, they become the law of the case.
Continuing on with the hypothetical, the highest court of the realm sustains the first of the first two trial errors that the intermediate court sustained, overrules the second of the three, and intentionally neglects or refuses to rule on the third overruled error. The intermediate court's rulings on the first and third point are the law of the case and cannot be reversed even though the highest court overruled the second of the first two errors.
Of course, the trial court has to follow the rulings of the highest court in the case, and, to the extent that the rulings of the intermediate court do not conflict with that of the highest court, the intermediate court's rulings are the law of the case.
Common-law courts love finality; once a potential error is waived or definitively ruled on by a higher court, the lower court judges are stuck with it.