If there are TV shows which will still be remembered in 150 years, Star Trek
has a reasonable chance of being among them. The question is how many people will watch it outside of intellectual/academic circles.
I mean, how many "average" people are seeing Le Voyage dans la lune
As for question whether Star Trek
will still be "in production" in some form... uh, we don't even know what kind of media/entertainment people will have.