There are two ways to look at this question: From a business perspective, and from a creative perspective.
From a business perspective, you have to start by looking at the recent history of the franchise and the current marketplace. Star Trek on TV was losing more and more viewers as time went by, until the final series Enterprise was canceled. Was this an indication of declining interest, quality, or both? I won't debate the quality question, but will say that viewership for almost ALL shows was declining in the last years of Enterprise, and has continued to decline since (even hit shows have less "eyeballs" than even five years ago).
So, you have declining viewership to deal with. Home video sales of TV seasons, once a fat profit center for studios, has become far less so as well (with the advent of streaming and a weak economy, many fans skip buying the series of DVD or bluray). Star Trek as a licensed property (for books, games, toys, T-shirts, etc.) is still pulling in a nice "annuity" for Paramount… would a new series provide for additional licensing opportunities? Sure, but licensing fees won't cover the production cost of a show (unless it's incredibly popular or the show is very cheap to produce).
That last point is key: Even if you take advantage of standing sets, costumes, and props, a Star Trek show is very expensive show to make, and requires a big investment… and because of the many reasons cited above, Hollywood is in a very "risk averse" phase right now. If a TV producer has to choose between an expensive SF show or a three-camera sitcom, a cop show, or a reality show… they'll pick the cheap show. One can make an argument that Star Trek has a built-in audience, one that will show up week after week… but the counter arguement is a very blunt one: when Enterprise was on the air, the ratings weren't there… and the ratings have not been there for other SF shows such as Fringe or Terra Nova.
And not just ratings, but demographics: Are Star Trek fans in that desirable 18 to 35 demographic? Based on my research, the JJ Abrams 2009 Trek movie brought a LOT of new fans to the franchise… and many of them are in that coveted group. Will they tune in to a TV show every week, though? That's a big question.
So, is there a business reason for Star Trek to be on TV again? Maybe, if the numbers work out. How can they? The obvious solution is an animated series, a la Star Wars The Clone Wars. It would be cheaper to produce, it would allow the producers the opportunity to do scenes and aliens that would be difficult to do in live action, and if it strikes the right tone it could appeal to adults and kids alike. And the upside to an animated series is it would helps grow the fanbase in a different way than a new film does. It wouldn't be prime time Star Trek like we've had before, but it would still be Trek on TV again.
Now, the creative question: Are there any more stories to be told? Can a new Star Trek series again take us to where no one has gone before? It depends on the talent involved. A good example when it comes to this is the other famous SF TV franchise, Doctor Who. The show has had various showrunners over the years, and many episodes were really bad… But even some of the best creative people can have a bad day. The deeper problem occurs when you have bad SEASONS, not just the occassional episode. This happened on Doctor Who, and this decline in quality led to declining viewers and the halt in production for several years.
I bring this up as a case study of what to avoid. If you get the wrong showrunner and writing staff behind a new Star Trek show, then you will sabotage the notion before it even begins. There's always possibilities, Spock said… possibilities to tell good stories with interesting characters in the Star Trek universe. Go forward thousands of years past Kirk and Spock, do an anthology show with different ships and crews on different misisons, do a Starfleet Academy show, do a Starfleet Black Ops show… There's lots of "space" to play in.
If you don't have the talent to tell such stories, though… then you shouldn't even try.