The way I understand this page about GFCI outlets: (a) GFCI outlets can fail after about 10 years, making them unable to detect faults, (b) when outlets made after 2006 fail, they shut off power automatically, and (c) pre-2006 outlets fail silently: they can't detect faults but they continue to provide power. That seems like a big safety hazard, and a good reason to replace my old GFCI outlets before they fail.
However, I haven't found anyone recommending proactive replacement, and if this was a legitimate safety concern I'd expect people to shout it from the rooftops. So are the old outlets worth replacing? Or am I just getting worried over nothing?
The GFCI outlets in my house were installed in the mid-90s (in the USA). And they're passing the tests with a GFCI outlet tester.