Laudator Temporis Acti

R.D. Dawe on Sophocles, Oedipus Rex 177 (LSJ definitions in square brackets added by me):

ἀμαιμάκετος is a Homeric word, of uncertain meaning, used again at Oed. Col. 127. It has been linked with words as diverse as αἷμα [blood], μάχη [battle], μῆκος [length] and μαιμάω [be very eager, quiver with eagerness], and when used of the Chimaera or her πῦρ [fire] was glossed by φοβερός [fearful], χαλεπός [difficult], ἀκαταπόνητος [inexhaustible] and ἀπροσπέλαστον [unapproachable]. Chantraine calls it 'terme poétique traditionnel et expressif dont le sens originel est ignoré de ceux qui l'utilisent'.

Cambridge Greek Lexicon:

ἀμαιμάκετος η ov (also ος ov) ep.adj. [pop.etym.: intensv.prfx., μαιμάω; also privatv.prfx., μάχομαι] (of the Chimaira, Nemean lion, Erinyes) app. formidable, awesome, irresistible Il. S. Theoc.; (of Poseidon’s trident, a spear) Pi. AR.; (of fire) Hes. S.; (of the sea) Hes. Pi.; (of the motion of the Clashing Rocks) Pi.; (of a goddess's might) Pi.; (of strife) B.; (of a ship's mast) perh. mighty or solid Od.

Franco Montanari, The Brill Dictionary of Ancient Greek:

ἀμαιμάκετος -η -οv [see μαιμάω?] irresistible, invincible IL. 6.179 (Chimera) PIND. P. 1.14 (sea) SOPH. O.T. 177 (fire), O.C. 127 (Furies) etc.; νεΐκος ἀ. persistent strife BACCHYL. Epin. 11.641 || strong, firm: ἱστόν ἀμαιμάκετον νηός the solid mast of the ship OD. 14.311.

Liddell-Scott-Jones:

ἀμαιμάκετος , η, ον, also ος, ον Hes.Sc.207:— irresistible, old Ep. word, also in Lyr. and Trag. (lyr.); of Chimaera, Il.6.179, 16.329; of fire vomited by her, Hes.Th.319; of fire generally, S.OT177; θάλασσα, πόντος, Hes.Sc.207, Pi.P.1.14; of ship's mast, proof against any strain, Od.14.311; of the trident, Pi.I.8(7).37; ἀ. μένος, κινηθμός, P.3.33, 4.208; νεῖκος stubborn, B.10.64; of the Furies, S.OC127; ἀ. βυθοῖς in unfathomable depths, IG3.900. [Usu. derived fr. ἀ- intens., μαιμάω, i.e. furious; but apptly. connected with ἄμαχος by Poets.]

Hans Christian Albertz in Lexikon des frühgriechischen Epos: Diccionario Griego–Español: