Movies from the iTunes Store stay available to play as much as you like for 48 hours, from the moment that playback is started.
If you want to play or resume after the 48 hour mark, then you would be prompted to pay for it as for any other new movie.
If you rent earlier than intended playback, in preparation, then make sure to not start playback right away, and choose “watch later” instead, to not start the 48 hours timer early.
Rent movies from the Apple TV app - Apple Support
When you rent a movie, you have 30 days to start watching it. As soon as you play your rental, your rental is available for 48 hours. Your rental automatically deletes from your library 30 days after you rent it or 48 hours after you start watching it, whichever is sooner.