In Doctor Who, the Doctor and his companions are replaced whenever actors wanted to leave, and this has allowed the show to go on (with a decade long hiatus) for almost 50 years.
So what if Star Trek did that same sort of thing, keeping in mind it somehow getting that constant longevity? Shatner wants to leave in season 7, another Captain comes on or Spock gets promoted, crew come and leave as actors get bored or want to leave, and the crew and ship are constantly dynamic and moving forward in time like an actual ship would. Could that at all work?