you mean "The Time of Rebirth"? the answer was Teleport, but a Week/Month would be better for this kind of story's
You're right on both but these aren't the only series that use a groundhog day setup centered around 24hrs and I always thought that the time limit range was too restricting.
And I don't know if I should even get into the psychological aspect of a never-ending 1000-year day, that would just make any person go insane. In the end, it's like other time regression series with a different range, on one end it's groundhog day level on the other it's you get to redo your life one more time. If the groundhog day series extended the frame from 24hrs to like a week/month or even a year as you said and reduced the ridiculous 1000 years length I think the series and others would be more believable. I know that other series like Wuxia center around unthinkable amounts of time so I guess they can slide.
Sorry for the rant.