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I read a sci-fi story in a collection of shorts about 10 years ago, I believe they were stories from 70s possibly and have been trying to track down the title.

My recollection is that a number of ships encountered problems with a black hole or similar timey-wimey space object, and the ship belonging to the protagonist's girlfriend/love interest sacrifices itself to save the others. The 'black hole's' properties being what they are, the man goes on to live his life on Earth where the ship is visible in space, stuck in the moment of their sacrifice forever.

Are you thinking of Gateway by Frederick Pohl?

Gateway is a space station built into a hollow asteroid constructed by the Heechee, a long-vanished alien race. Humans have had limited success understanding Heechee technology found there and elsewhere in the solar system.

The main character is Robinette Stetley Broadhead — known as Robin, Rob, Robbie, or Bob, depending on circumstances and his state of mind. He is a young food shale miner on Earth who wins a lottery, giving him just enough money to purchase a one-way ticket to Gateway.

He develops a relationship with a woman named Klara who works on the space station.

When the ships arrive, their crews find to their horror that they are in the gravitational grip of a black hole without enough power to break free. The crews devise a desperate escape plan: Move everyone into one ship and eject the other toward the black hole, thus gaining enough of a boost to escape. Working frantically to transfer unnecessary equipment to make room, Broadhead finds himself alone in the wrong ship when time runs out. He closes the hatch so that the plan can proceed. By chance, his ship is the one that breaks free, leaving the rest of the crew falling into the black hole.

Broadhead returns to Gateway and receives the entire bonus. He feels enormous survivor guilt for leaving his crewmates, especially Klara, and is unsure whether he intended to sacrifice himself or the others.

Sounds a lot like Poul Anderson's short story "Kyrie", which was the (unaccepted) answer to this old question. Does any of these covers look familiar?

He had not really understood what it would mean to confront something so violent that space and time themselves were twisted thereby.

His speed increased appallingly. That was in his own measure; from Raven they saw him fall through several days. The properties of matter were changed. He could not push hard enough or fast enough to escape.

Radiation, stripped nuclei, particles born and destroyed and born again, sleeted and shouted through him. His substance was peeled away, layer by layer.The supernova core was a white delirium before him. It shrank as he approached, ever smaller, denser, so brilliant that brilliance ceased to have meaning. Finally the gravitational forces laid their full grip upon him.

—Eloise! he shrieked in the agony of his disintegration—Oh, Eloise, help me!

The star swallowed him up. He was stretched infinitely long, compressed infinitely thin, and vanished from existence.

[. . . .]

Szili made soothing noises and left. In the corridor he encountered Mazundar. "How is she?" the physicist asked. The captain scowled. "Not good. I hope she doesn't crack entirely before we can get her to a psychiatrist."

"Why, what is wrong?"

"She thinks she can hear him."

Szili braced himself and waited.

"She does," Mazundar said. "Obviously she does."

"But that's impossible! He's dead!"

"Remember the time dilation," Mazundar replied. "He fell from the sky and perished swiftly, yes. But in supernova time. Not the same as ours. To us, the final stellar collapse takes an infinite number of years. And telepathy has no distance limits." The physicist started walking fast away from that cabin. "He will always be with her."