Despair - Vine's Expository Dictionary of New Testament Words
Despair[ 1,,G1820, exaporeo ]
is used in the NT in the Passive Voice, with Middle sense, to be utterly without a way" (ek, "out of," intensive, a, negative, poros, "a way through;" cp. poreuo, "to go through;" (Eng., "ferry" is connected); "to be quite at a loss, without resource, in despair." It is used in 2 Corinthians 1:8, with reference to life; in 2 Corinthians 4:8, in the sentence "perplexed, yet not unto (AV, "in') despair," the word "perplexed" translates the verb aporeo, and the phrase "unto despair" translates the intensive form exaporeo, a play on the words. In the Sept., Psalms 88:15, where the translation is "having been lifted up, I was brought low and into despair."
[ 2,,G560, apelpizo ]
lit., "to hope away" (apo, "away from," elpizo, "to hope"), i.e., "to give up in despair, to despair," is used in Luke 6:35, RV, "nothing despairing," i.e., without anxiety as to the result, or not "despairing" of the recompense from God; this is probably the true meaning; AV, "hoping for nothing again." The marg., "of no man," is to be rejected.