Downtiming the Night Side by Jack L. Chalker 1985
When former Air Force officer and NSA agent Ron Moosic is assigned for special duty in charge of security for a nuclear power plant, he has idea that the plant is only a cover for a top-secret project involving time travel.
The government has discovered a way to travel back in time and is sending secret observers to different periods. But there are serious limitations with the time travelling process.
All travelers are automatically re-born into someone who is actually alive during the historical period, and staying in the past for too long causes memory loss and the risk of losing their own selves.
Suddenly Moosic is himself forced to travel back in time as terrorists infiltrate the facility. But little does he kw that both he and the terrorists are just pawns in a much wider game played by future beings a game that may result in the destruction of Earth itself.