Often, discussions about nuclear energy tend to run rampant with misinformation and hyperbole. I offer the following points for clarity, context, and thought.
1) Just to be clear: There are NO 80 year old reactors. If Chicago-Pile 1 was still operating, it would turn 70 this year. The oldest currently operating nuclear reactor is the Oyster Creek facility. This reactor came online December 23rd 1969 making it 42 years old curerntly. This is according to Wikipedia. http://en.wikipedia.org/wiki/Oyster_Creek_Nuclear_Generating_Station
2) All NRC regulated reactors have maintenance performed on the systems every outage, to the point that much of the facility is newer than the day it turned on. This is due to maintenance and repair activity, as well as upgrades to improve efficiency. The article calls this "midlife refurbishment". The industry does this because it is easier and less costly than a new reactor. The thought process of the industry is that it is easier to tear down and rebuild under the existing license than it is to get approval for a new license. If the industry could feasibly replace a reactor vessel, I would bet they would.
3) ASME Boiler and Pressure Vessel Code Section 3 is a good code. Creep, Fatigue, Corrosion, and many other issues are addressed in this code that the non-nuclear codes for B&PV only tough upon exotic need, and then refer the engineer to the section 3 code. I encourage you to read it.
4) Some reactor operators send material samples to the Advanced Test Reactor at the INL for accelerated radiation age testing. This information is sought by the reactor operators to gain a better understanding for themselves about their own equipment.
5) Reactors are designed for a much longer life than 40 years, but the NRC set the 40 year license to force a mid-life review. Reactors get far better treatment than any car or plane that most people have ever have ridden in. In this context, a 40 year old reactor properly maintained is very possibly not a safety concern.
6) The Davis-Besse RPV head mentioned by the article was a case of criminal conduct in the eyes of some people, and is not considered normal operating behavior by people I have met from the industry. Whatever the facts are, the indictment can be found here. http://www.corporatecrimereporter.com/documents/indictment.pdf
7) Reactors designed to operated under the NRC have a "defense in depth" safety approach. The reactor and facilities are given a design basis accident that is a conservative forecasting of potential accident scenarios.
8) The NRC has a glossary available to you http://www.nrc.gov/reading-rm/basic-ref/glossary.html note the term "meltdown" is not there. Many people associated with the nuclear field feel that it is a poor term that does not adequately describe a problem's behavior or severity. This is borne out of the use of the term for several reactor failures that all had different designs, behaviors, and severity of failure.
9) New reactor designs offer some stimulating improvements. The Generation 4 reactor effort can be found at http://www.gen-4.org/ currently the US is operating Gen 2 reactors.