Hi and welcome to the forum @Anonymous User,
Nothing stays on the NOW TV service forever. Unless otherwise stated, episodes from the newest season of most 'Entertainment' shows stay on the NOW TV service for around 30 days after their UK 'live' broadcast/streamed transmission date (much like they do with BBC iPlayer).
The series could re-appear at some time on the NOW TV service, either as 'live' streams or as a series 'box set' but only if a new agreement deal is negotiated with the content copyright holders. Or before the next new series begins - if there is one...
Why hasn't the new episode of Alaskan Bush People shown up on catch-up?
Two new episodes were transmitted on Thursday 2nd Nov - the Bushcraft Chronicles at 8pm (which is on catch-up) followed by a new episode "Faith and Family" at 9pm which isn't on catch-up.
I could have watched it live at the time but as previous seasons have been available on catch-up, I assumed this would be.