Trek's charm at this late date has very little to do with with its plausibility in any other than the most narrowly delineated of terms - we suspend our disbelief because the show entertains us.
Suspension of disbelief is a blurry concept in the context of science fiction refracted through decades of scientific progress.
Sometimes, scientific descriptions are proven wrong. Perelandra is difficult to believe once images from a Mars lander can be viewed. Almost all early computer renditions dramatically underestimated the difficulty of understanding ordinary speech (and dramatically underestimated the raw storage and speed of modern computers).
On the flip side, sometimes science that was meant to seem astounding becomes trite. Kirk with his communicators, Picard with his tablets, Nemo and his submarine: we find it hard to empathize with the seriousness with which what is now the mundane is treated.
TNG certainly must and will contend with these factors. As the notion of talking robots/AI trickles down over the decades from a rarefied academic discourse to a commonplace feature in Siri, many of the computer interaction scenes will be viewed increasingly as out of balance. What by dramatic emphasis seemed impressive sometimes seems dull; and non-specialists can easily see the technical flaws in, say, Data's set of flaws and strengths.
Without doubt, this progress does pose a challenge for TNG's relevance.
But where TNG shines, what it does in a way no sci-fi drama has done before or since, is to address skilfully complex timeless questions of character and humanity. The center of TNG is Picard, who is unique among the stars (except for Riker) in being limited only to human abilities. But at the same time Picard is routinely pitted against seemingly impossible problems or human dilemmas. How one negotiates with a stronger foe is an eternal problem; when to, say, capitulate and when not to. How to face a situation that in one sense Picard thinks is not important, or where he realizes his compatriots are living meaningless lives, is another eternal problem.
Through writing and acting, Picard demonstrates these concerns in ways that I think will resound for a long time. He gets by, surrounded by smarter, stronger, more powerful beings; placed in impossible situations, only through character. But he expresses that character incredibly well.
Picard does express these concerns so powerfully that his expressions are timeless. Should he help his friend or help his career in Measure of a Man? He is easily smart enough to rationalize either decision. In the "Geordi's eyes" scene you can see him wrestling with this decision, a prototypical human decision that has been and will be faced for centuries. In Inner Light, how does he respond to Eline's concerns, that he knows are meaningless if they exist at all? Does he focus on key philosophical issues (star-gazing, figuratively) or does he just focus on what seems to be actual happiness of his companions?
Old Shakespeare dramas are still routinely watched and studied, even though virtually none of us really understand the plausibility or nuances of medieval Venetian politics or Danish monarchies. Much of the plots, like an old scifi drama, fails to resonate. But the human questions, the struggles between love and family; between loyalty and advancement; are as relevant today as when the plays were written or are set.
It is no accident therefore that Stewart was a Shakespearean actor: his skill is in evoking timeless emotions, even in milieus that are alien to viewers (and ancient Venice is as alien to a twentieth century viewer as any starship). I realize that nearly all good sci-fi dramas try to concern themselves with universals, but among TV serials, only TNG has actually succeeded.
Stewart, with immeasurable help from Spiner as a kind of counterweight, expresses these problems and these emotions more powerfully, more accurately, and more intriguingly than any actor since. I predict, therefore, that despite the way that time will serve to alienate us perhaps from TNG's plot as time goes by, it will only highlight the real core of TNG: Picard's human struggles. And those struggles are timeless. So I think TNG will, or should, live for a long, long time.