That's "Lucifer!", a short shory by E. C. Tubb, first published in Visions of Tomorros #3, November 1969, available at the Internet Archive. Being in the US, you might have seen it in either the 1972 first printing or the 1975 second printing of the anthology The Year's Best Horror Stories, No. 1 edited by Richard Davis.
(Tubb's 1999 story "Fallen Angel" is a revised version of "Lucifer". I guess one or both of these stories could have inspired or influenced the 2013 Futurama episode "Meanwhile".)
The protagonist is working in a morgue when a body is brought in. The dead man was a jet-setter who was killed suddenly--hit by a bus, or something fell on him.
Like a steel cable snapping when the safe it was supporting hung twenty feet above the ground. The safe fell, smashing the sidewalk but doing no other damage. The cable, suddenly released from strain, snapped like a whip, the end jerking in a random motion impossible to predict. The odds against it hitting any one particular place were astronomical. The odds against one of the Special People being in just that spot at that exact time were so high as to negate normal probability. But it happened. The frayed end of the cable hit a skull, shredding bone, brain and tissue in an ungodly mess. A surgically implanted mechanism sent out a distress call. The man's friends received the signal. Frank Weston got the body.
While processing the body, the protagonist finds a ring on the body's finger and decides to keep it.
Sometimes, in his job, an unscrupulous man could make a little on the side. Frank had no scruples only defensive caution. The ring could have been lost before the stiff arrived in his care. The hand was caked with blood and maybe no one had noticed it. Even if they had it would be his word against theirs. If he could get it off, wash the hand free of blood, stash it away and act innocent the ring could be his. And he would get it off if he had to smash the hand to do it. Accidents sometimes made strange injuries.
Shortly afterwards, some jet-set friends of the dead man show up looking for the ring, but the protagonist feigns ignorance and the friends eventually leave.
"One moment." The two men looked at each other then the one who had spoken turned to Frank. "Our friend wore a ring. It was something like this." He extended his hand. "The ring had a stone and a wide band. Could we have it please."
Frank was stubborn. "I haven't got it. I haven't even seen it. He wasn't wearing it when he came in here."
The man discovers that squeezing the ring lets him relive the previous minute of his life, and he can live that minute differently.
He frowned and tried again. Abruptly the man was back at his table. He rose, stretched, headed towards the door. Frank pressed the stud and held it down, counting. Fifty-seven seconds and suddenly the man was back at his table again. He rose, stretched, headed towards the door. This time Frank let him go.
As I recall, he uses the ring to seduce a woman by refining his technique until it works, so to speak.
He reached out and took her in his arms, heart still pounding from the pleasure of having inflicted pain. He kissed her with practiced skill, nibbling her gently with his teeth. He ran his hands over her body, thin material rustling as it fell from her shoulders. He bit a little harder and felt her tense.
"Don't do that!" she said abruptly. "I hate anyone doing that!"
One bad mark. Frank counted seconds as he reached for the light switch. With darkness she squirmed, pushed herself free of his arms.
"I hate the dark! Must you be like all the others?"
Two bad marks. Twenty seconds to go. Time for one more quick exploration. His hands groped, made contact, moved with educated determination. She sighed with pleasure.
He activated the ring.
"Frank!"
He reached out and took her in his arms, this time making no attempt to either nibble or bite. Her clothing rustled to the floor and the skin gleamed like pearl in the light. He looked at her, boldly admiring, and his hands moved in the way which gave her pleasure.
Later, he uses the ring to win big at a casino. Soon the man is on his way to being a member of the jet set himself.
Luck, the fortuitous combination of favourable circumstances, but who needs luck when they know what is going to happen fifty-seven seconds in advance? Call it a minute. Not long?
Try holding your breath that long. Try resting your hand on a red-hot stove for even half that time. In a minute you can walk a hundred yards, run a quarter of a mile, fall three. You can conceive, die, get married. Fifty-seven seconds is enough for a lot of things.
For a card to turn, a ball to settle, a pair of dice tumble to rest. Frank was a sure-fire winner in more ways than one.
Finally he's on a plane, flying to Europe or some place. There's an in-flight emergency and the plane breaks up in mid-air.
Something hit the roof of the cabin. There was a ripping sound, a blast of air, an irresistible force which tore him from his seat and flung him into space. Air gushed from his lungs as he began to fall.
The man finds himself doomed to keep squeezing the ring, as I think the last line goes, "because the alternative was to fall into the waiting sea".
The clouds passed. Below the sea spread in a shimmer of light and water. His stomach constricted with overwhelming terror as he stared at the waves, his lurking acrophobia aroused and tearing at every cell. Hitting the sea would be like smashing into a floor of solid concrete and he would be conscious to the very end. Spasmodically he activated and immediately was high in the air again with almost a minute of grace in which to fall.
Fifty-seven seconds of undiluted hell.
Repeated.
Repeated.
Repeated over and over because the alternative was to smash into the waiting sea.
