I read this sometime in the 1990s; I don't recall if it was in an anthology or a magazine.
A guy has recently gone through a bad break-up, and desperately misses the good times that came before. He is introduced to a drug that allows him to completely re-experience his memories, as though he were actually present again for them. The catch is that the memories pass at an accelerated rate (e.g. 4 times as fast as the actually happened) and once he starts he can't wind back to an earlier time; the memories are retrieved strictly sequentially.
After some months of reliving his relationship he starts to relive the break-up, but for some reason he keeps going. He re-experiences his loss and desolation, and then he starts re-experiencing his relationship all over again, by reliving his memories of his previous replay.
In the present day he is in a darkened room with the shades drawn, and a shaft of light forms a shape that makes him think of a someone running across the wall.
The guy is now a complete addict and keeps taking the drug, experiencing shorter and shorter loops as he inevitably catches up to the present. The story highlights his last trip, as iterations last minutes, then just a minute, then seconds, as he repeatedly layers level after level of experience in shorter and shorter times...
The story essentially breaks off there, with the closing line being approximately "The runner persisted; there wasn't anything else it could do."
There was one notable aspect of the text layout for the story; within the drug experience, every time he ran through the loop his new thoughts would be shown added to his thoughts from previous iterations. Something like:
A thing happened
He remembers how this made him feel
He thinks about why he felt that way
Why did that thing happen?
Would things have been different if...
I may be conflating this with a different story, but it's possible that on subsequent visits to events he was able to observe more, and it changed his understanding and feelings of what happened. If on the first pass he remembered with glee putting someone down, by the third or fourth iteration he was realising how hurtful he had been.
I had thought the title might have been "The Runner" but a search on ISFDb doesn't find it.