The issue with the Dome (and why this is brought up even though it's not old by most standards) is how it was built. The Dome was built in an architectural dark age, with a design that won't last the test of time. It's a concrete sarcophagus. Unlike something like the Horseshoe, it is not amenable to renovations to expand, remodel, or anything like that. It is quite literally designed to be destroyed or kept as is. Thus, while something like Bryant Denny or the Shoe can be upgraded to be more modern over time, you can't really upgrade or renovate the Dome in the same way. You can't expand the concourses, you can't replace the roof, you can't do a lot of things other than room remodels, new seats, and things like that. This is why the new stadium talk constantly comes up, because it's the only logical next step. Most importantly with a new stadium, it needs to be built to allow renovation and redesign, rather than a more fixed design like the Carrier Dome.
Oh, and a new stadium could have a new sponsor.