What does μὴ ἐγκακεῖν mean in Luke 18:1?

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What does μὴ ἐγκακεῖν mean in Luke 18:1? (Greek text from NA27)

Note ἐγκακέω is the preposition ἔν combined with the verb κακέω. In BDAG “ἐγκακέω is defined as 1. become weary, tired w. ptc. foll. … 2. lose heart, despair …; be afraid, of women in child-birth …” (1979 ed., p 215). The verb κακέω doesn’t occur in the New Testament, but the adjective κακός, ή, όν (bad, worthless, inferior BDAG) does. This adjective is the opposite of καλός, ή, όν

καλός, ή, όν: pertaining to having acceptable characteristics or functioning in an agreeable manner, often with the focus on outward form or appearance—‘good, fine.’

Louw, J. P., & Nida, E. A. (1996). Greek-English lexicon of the New Testament: based on semantic domains (electronic ed. of the 2nd edition., Vol. 1, p. 622). New York: United Bible Societies.

κακός, ή, όν; κακῶς: pertaining to having experienced harm—‘harmed, harm, injured.’(Ibid., Vol. 1, p. 229)

An example of how these words are used, if food tastes good, it is καλός, while if food tastes bad it is κακός.

I wondering, since κακ is the root of ἐγκακέω, if this word has a fuller meaning than the translations of “to not be weary” or “to not despair” and means “to not be weary of bad, distasteful, and hurtful circumstances.” This fuller meaning does seem to match the parable. However, the fuller meaning could also mean becoming weary of praying and viewing prayer as drudgery (e.g. Gal. 6:9; 2 Thes. 3:13). Maybe someone with a classical Greek background knows more usage of this word.

Supplemental information: The other five New Testament passages with ἐγκακέω. In all six New Testament occurrences it has a negative adverb μὴ or οὐκ.

Therefore, since we have this ministry because we were shown mercy, we do not give up. Instead, we have renounced shameful secret things, not walking in deceit or distorting God’s message, but commending ourselves to every person’s conscience in God’s sight by an open display of the truth. (2 Cor. 4:1–2, ESV, translated give up)

Therefore we do not give up. Even though our outer person is being destroyed, our inner person is being renewed day by day. (2 Cor. 4:16, ESV, translated give up)

So we must not get tired of doing good, for we will reap at the proper time if we don’t give up. (Gal. 6:9, ESV, translated get tired)

This verse seems to not match because the object is “doing good” (καλὸν ποιοῦντες). However, how the verb matches κακός here is the idea of letting doing good become unpleasant or distasteful, a drudgery; the opposite of the idea in cheerful giver.

So then I ask you not to be discouraged over my afflictions on your behalf, for they are your glory. (Eph. 3:13, ESV, translated be discouraged)

Brothers, do not grow weary in doing good. (2 Thes. 3:13, ESV, translated grow weary)

This has the same sense as Gal. 6:9.