Though the question belongs more in Biblical Hermeneutics or even the Christianity SE, given that the Septuagint as we have it today is a Christian text, as the question hasn't been closed and/or moved yet, I'll try to answer. The short answer is that we don't really know why this is the case, although a couple of attempts to explain this have been made over the years.
Long answer: The Septuagint as we have it today is a composite work: It was made by a number of Church Fathers who took several manuscripts of septuagints - i.e., Greek translations of Tanach named after the original, long-lost Septuagint - and merged them together. This was done because by their time (circa the 4th-5th centuries and onwards) there were too many Greek translations running around, some with problematic translations (in the eyes of the Church). So a number of prime manuscripts were chosen and used to create a new, eclectic septuagint, which is how we have the Septuagint today. This Septuagint is, therefore, primarily Christian in origin and character, but at least in one case, it preserves a Jewish translation tradition (see here and here for more info). You can read a bit about the development of the Septuagint as it is today in Britannica's entry on the Septuagint (which I find to be shorter and simpler than Wikipedia's entry).
Now, there are a number of differences between the modern Septuagint and the Jewish Tanach, one being this missing verse. Emanuel Tov, who is probably the world's top (academic) scholar of the development of the biblical text and the various variants that have evolved from it (Samaritan, Christian, Qumran, etc) discussed this in the past, and has made that discussion available online. His conclusion, as is nowadays pretty much a common consensus in the academic world, is that the septuagint manuscripts were based on a version of the Hebrew text that simply did not have this verse in the first place (a "Vorlage"). But as there are several other missing verses, it is difficult to argue logically that this original text was copied by a scribe that mistakenly omitted that verse. He argues that even after the final editing of Proverbs, older versions were still running around and being used by people, and naturally were also used to make more copies. And one of those pre-final versions eventually became the base manuscript for what is now the Septuagint's Proverbs.
All of this of course means that it is entirely possible that some of the older Greek Proverbs manuscripts did have this verse (as well as the other missing ones), but the particular manuscripts that reached the hands of the Church Fathers and were incorporated into the eclectic version simply did not.
I myself am not sure about his theory about pre-edited versions of Proverbs running around as late as the 2nd century BCE (the time thought that Proverbs was translated into Greek), but he does have a point in that the significant differences between Septuagint Proverbs and Masoretic Proverbs make it difficult to claim that this is merely scribal error.
Aharon Kaminka in his essay on the subject in the Hebrew journal Sinai, vol. 8 (1941), pp. 284-285 suggested that some of the changes may be put down to the translator's inability to properly translate certain verses into Greek. It's possible that this was the reason for the disappearance of this verse. This would tie in with the low quality of Greek translations that the Church Fathers saw running around.1
1 Bear in mind that Kaminka wrote this essay a number of years before the first trove of Dead Sea Scrolls was discovered, and never mind later troves. In the DSS there have been found some Hebrew Tanachic manuscripts that bear some similarity to the Greek septuagints. Chapter 22 of Proverbs has not been found (see here for which parts were found), so we can't say what this section of Proverbs looked like for the sect(s) of Qumran, but in general, these partial similarities between some of the Hebrew DSS and the Septuagint make it more difficult to believe that these differences from the MT are merely from scribal error or translation difficulties.