Where I think a lot of campaigns fizzle out is because the DM and/or group hasn't thought about the real time commitment being made and whether that is sustainable for the given group.
I think the best option is to conceive of the end state of the game in terms of real time (hours, weeks, months, years, sessions or perhaps levels) before the campaign begins, then shave a few sessions off of that. Better to leave them wanting more than to let it die on the vine.
Unless one's intention going in is specifically to leave the duration open-ended, to last the shorter of a) as long as anyone wants to play it or b) the DM's life.
That's how I've approached every campaign I've run.
So, in answer to the OP: re-starts with new characters within the same setting/campaign can work, even better if you can somehow link the re-start group to what went before (or is currently ongoing) in previous play.
I did this not so long ago: restarted within the same campaign, and sent the party into an adventure that had already been done 5 in-game years earlier by a different group! (long-term player turnover has its benefits!) They never figured out why/how the place had reset itself, but every time they took anything significant back to town they kept getting "Hey, we've seen this before! Some boneheads brought us the same thing five years ago! What the ... ?"
Another option is to allow/encourage players to have more than one character on the go, and split them into multiple parties. That way, you can in effect run the same in-game time period a few times over, as during the same spring that Party 1 is busy vanquishing Snurri the Frost Giant Party 2 can be off dealing with Captain Barbosa the pirate lord. In real-time, however, you run one party through its adventure then jump to the other party and run that; the trick for you-as-DM is to not let the two (or more!) groups get too far separated in in-game time, and believe me whenI say that can become a real juggling act.
I should also ask of the OP: is the game getting long in the tooth in your eyes as DM or in the eyes of the players? If it's the players saying it's getting old the above ideas can work to refresh things; if it's you-as-DM who's had enough then its days may well be numbered, as there's no point running something you're not enjoying. I've had two long ones go this way. One I brought to a story-based shut-down conclusion while the other I just left hanging; the advantage of doing the latter is that characters from that game remain available for play in later/other campaigns if desired.