There are perhaps two perspectives here.
- the franchise is alive only as long as there are big new things introduced.
- the franchise is alive as long as interest is maintained/continued.
Well, I think both are correct (remove "big" and replace with "official" in your first one). But in the second sense, Metropolis is still alive, even though the last and only movie was made way back in 1927. Oh, there's "interest", sure.
I don't deny that the people who loved Star Trek before continued to love it. But the point is that the series and movies (the meat of the franchise) were no longer making good money. In that respect, Abrams and his collaborators "brought back" Star Trek.
Now, I don't think Paramount would've let the franchise lay there for too long before trying again, but if the 2009 movie had bombed, that might've been the deathknell for Trek.