The protagonist despairs, perhaps after a war. He contemplates suicide when he is called to rescue a man stuck out on a snowy mountain. The phrase that occurs to me is "The Razor's Edge", but it isn't that story. He could die on this ridge. He is not afraid of death; he finds a spiritual elation in this rescue quest. At the end he decides that if life can contain that feeling, it is worth carrying on. What are we missing in the fears that limit us? I read the story in a book of short stories selected for an elementary "Great Books" group in probably the late 1960's. The anthology had "Action" in the title.
There's the C.E. Montague's short story "Action", which fits some of the details.
From Reconstructionary Tales blog post:
Christopher Bell, ‘reigning sovereign’ of a dynasty of Manchester merchant princes, who wakes one morning to feel a numbness down one side of his body. He has fought in the Great War, during which he lost his beloved wife, and is a keen climber. Facing a future of invalid-chair and male nurse, and after a couple of humiliating allowances being made for his condition, he revolts. He won’t commit suicide but, reading of a great climber’s ‘greatest adventures’, Bell wonders how big a margin of safety had attended that successful expedition: ‘what if such a party were to try paring and paring away at that pretty wide margin?’ He returns to an old haunt, Zinal, in the Swiss canton of Valais, in late September. His target is a glacier with ice ‘steep and bare and blue’—with an overhang: ‘nowhere in the whole thousand feet of ascent would a man have a foothold to stand on, unless he made it.’ He climbs conscientiously until genuinely exhausted: ‘that was the end, he felt, of all possible effort’. Then a falling ice-axe and the standard Alpine cry for help, alerts him to a drama just above the overhang: a woman at the end of a rope which her husband desperately hangs on to above her. Bell is galvanised into heightened, unthinking action, and all three are eventually saved. In the Weisshorn hut, while she sleeps, he tells the man, Gollen, who’s a doctor, his symptoms. Gollen talks about artists, saints, raised to the uttermost through action, ‘“every bit of your consciousness taken up into some ecstasy of endeavour that’s passion and peace.”’ Looking out at the mountain under the moon, Gollen asks, when Bell says it’s ‘all right’, whether it’s all right enough. Bell says oh yes, he’s ‘sticking on’.
It can be read on archive.org.