They wont just stop, Star Trek will always live in some form or another.
Especially because of the existence of Star Wars and it's continued future. Yeah, they could go on to yet a different universe for a TV series.
But the JJ-verse is dead already. It isnt Star Trek. Only in name. I think this Axanar thing proves there is still a lot of life in the Prime universe. Even the original TOS is still being made at Phase II. They are already 4 years into the 5 year mission never completed by TOS. The project is going to complete after the 5 year mission is over, and it will tie into the beginning of the Prime Universe at some point.