If you're talking a 'romantic' series, I'd agree. There's only so long the 'will they or won't they' vibe can stay interesting. So you either have to just let them get together or split them up. Which will annoy half the readership either way.
What can work indefinitely, I think, are mystery series. If you make the MC someone who it is not surprising to continually find dealing with murders (a detective, lawyer, other law enforcement officer, etc.) you can build a good cast around them and make each new MYSTERY fresh while keeping the characters mostly familiar. The key is to keep the peripheral story arcs extremely peripheral! I think Linda Fairstein does this well with her Alex Cooper series.
A lot of TV shows have problems with this nowadays. Used to be you'd watch
Magnum PI,
Matlock,
Columbo or
Murder She Wrote (though trouble certainly followed that ol' gal and Cabot Cove must have the highest
per capita murder rate in the country.

) and you'd know you'd see the same cast of characters each week with a new baddie or group to take down. You could actually watch them in any order -- so if you miss this week, you'd see it in re-runs in the summer and not miss a thing.
But now, most of them have these over-riding story arcs that, if you miss one episode you can be partially lost. And some are absolutely serials to where you shouldn't even expect any sort of resolution to ANYTHING until the very end -- and missing one episode means you're
totally lost!

That's fine, if that's what you signed up for, but annoying if you just want to sit down and, say, watch an episode of something that happens to be showing in syndication. I'm guessing it's because so many people have digital recorders nowadays, so the assumption is that people will record and watch in order. But I find I really lose interest when the 'mystery of the week' becomes so obviously secondary to whatever bigger story they think they're trying to tell. Especially if the characters are not particularly endearing. I've pretty much given up on both
Suits and
Covert Affairs for that reason, and if it wasn't the last season of
Burn Notice I'd have given up on it as well.