I read this book series around 1950; I think there were only 2 books in the series. Scientists' brains are transferred into a space-exploring robots which would last for thousands of years. When the robots finally failed mechanically, the human brains would be transferred to new robots, allowing the scientists to live for tens of thousands of years and continue exploring the Galaxy.
This is a story that has many similarities with the cycle of Professor Jameson, by Neil R. Jones, which was very popular in the magazine "Amazing Stories" in the 1930s and 1940s and could, perhaps, be edited as books in the 1950s.
In the first of these stories, Professor Jameson was a dying man who had his body preserved inside a satellite orbiting the Earth. Millions of years later his body is found by an extraterrestrial expedition of Zoromes.
The Zoromes were originally organic beings and reached immortality by transplanting their brains into autonomous machines. When they find Jameson's body, they do the same with his brain, bringing him back to life and inviting him to join their eternal exploration of the Galaxy.
Neil R. Jones wrote more than 30 stories about Professor Jameson and his companions. I see in wikipedia that they were compiled into books in the 1960s. Here are the covers from then in case they bring back any memories of you.
I don't know if there are any previous editions. I only have read the first story of all, "The Jameson Satellite", which was included in an anthology by Isaac Asimov.
There is an Outer Limits episode, The Brain of Colonel Barham with a similar plot. I think there were also several other episodes of that series with a roughly parallel theme. It could be that the story you seek was adapted to TV in one of those episodes.