The Greek verb exaporeomai (ἐξαπορέομαι) means to be utterly at a loss or to despair completely with no way out. The compound ex-a-poros (out-without-way) captures complete roadlessness. It appears twice in the New Testament, both in Paul.
Paul's two uses are theologically decisive. In 2 Corinthians 1:8, he writes that they were "utterly despairing even of life" — brought to the absolute end of their resources. But this is the purpose: "that we should not trust in ourselves, but in God which raiseth the dead." The experience of utter exaporeomai is the school of resurrection faith. 2 Corinthians 4:8: "perplexed but not in utter despair."