Aquila1 translated the Hebrew מַרְגֵּעָה into Greek as ἀνάψυξις, meaning “cooling, relief, respite”;2 the Vulgate, refrigerium, which is essentially the equivalent of the Greek ἀνάψυξις;3 Symmachus, ἠρεμία, meaning “rest.”4 The Isaiah Dead Sea Scroll (1QIsaa) has the same Hebrew word in question.

According to Gesenius, מַרְגֵּעָה is derived from the verb רָגַע. This verb seems to have a connotation of stillness. In binyan Nifʿal, it can mean “to rest or be still.”5 In binyan Hifʿil, it can mean “to still, make still, to give rest” (transitive) or “to rest, dwell quietly” (intransitive).6
So, why σύντριμμα? σύντριμμα can mean destruction or ruin, but also break or fracture. The related verb is συντρίβω, which can mean “to crush, shatter, break.”7 It seems to me that the only plausible reason for σύντριμμα (however wrong it may be) in Isa. 28:12 is that the translator derived its meaning from רָגַע in Job 7:5. Whether it truly means “broken” there is arguable, but it seems the committee that produced the King James Version thought so.
Footnotes
1 Field, p. 479
2 LSJ, p. 127
3 Lewis & Short, p. 1548; cf. 2 Tim. 1:16
4 LSJ, p. 777
5 Gesenius, p. 507
6 ibid.
7 BDAG, p. 976; LSJ, p. 1728
References
Arndt, William; Bauer, Walter; Danker, Frederick William. A Greek-English Lexicon of the New Testament and Other Early Christian Literature. 3rd ed. Chicago: U of Chicago P, 2000.
Field, Frederick. Origenis Hexaplorum. Vol. 2. Oxonii: E Typographeo Clarendoniano, 1875.
Gesenius, Heinrich Friedrich Wilhelm. Gesenius’s Hebrew and Chaldee Lexicon to the Old Testament Scriptures. Trans. Tregelles, Samuel Prideaux. London: Bagster, 1860.
Lewis, Charlton T.; Short, Charles. Harper’s Latin Dictionary: A New Latin Dictionary Founded on the Translation of Freund’s Latin-German Lexicon. New York: American Book, 1879.