story identification - Time traveling astronaut appearing frozen to observers in time travel accident

So I was recently watching the series seven episode of Doctor Who titled "Hide" and it struck me that I had read a short story that was remarkably similar to the astronaut woman of the episode.

Here's what I remember definitively of the story:

The story is told from two perspectives: that of the traveler and that of the observers throughout time. The traveler is running but to the outward observers he/she appears frozen like a statue. As the story progresses the 'statue' moves slowly through the millenia but to the everyday people its imperceptible, he/she is just an anomalous statue.

What I think I remember:

The time traveler is dressed in some type of space suit looking thing. I think the time traveler is the test pilot for the new time travel device/ship. The traveler may possibly be crossing dimensions (really not sure about that). They are either running towards a light or away from the crashed ship. I vaguely remember something like the traveler was trying to send a message or something to a loved one but the distortion made it unintelligible to the receiver but by the end of the story someone had cracked it and it may have been something like "i love you, goodbye." or something to that effect.

I'm also assuming that, from my vague recollections of the story compounded with what has now been years of studying SF, that this story fits into the 50's or 60's. While I think it could easily have been written as early as the 40's I don't think it would have been written in the 70's.

Thanks in advance for the help, because this is driving me insane that I can't remember more about this story.

Answer

It's not an exact match, but it sounds a bit like "The Man Who Walked Home" by James Tiptree, Jr as found here.

The Man Who Walked Home • (1972)

Caught in a time travel experiment gone wrong, John Delgado walks home from the unimaginably distant future. To him, it takes only seconds, but on Earth years, decades and centuries see him walk in reverse, appearing once a year at the same spot, myths, legends and religions growing up around him.