Most of the older plants have had their license extended to 60 years. Some are requesting an extension to 80 years because everything is working just fine.
That's not safe, though, because you can't perform a complete metallurgical inspection of the interior of the reactor, and it tends to be damaged over time. Also, many of our older reactors are based on unsafe designs; that they haven't had an incident is laudable, but that they won't have a serious one in the future is still not assurable. And a number of them are proven insecure designs, literally based on the same design as used at Fukushima Daiichi and also storing spent fuel on site.
I am not wholly against nuclear power, but I am wholly against extending the lifespan of old reactors which frankly weren't safe when they were built. That human ingenuity has kept them going is not a counterargument. It is pucker-inducing.