I fielded tech support questions from an app that had grown to send email. Every week we got a couple of emails from some time on January 1, 1970, each from a new person, and a whole slew of people whose batteries were on the edge of failing and so their machine was days or months off from reality.
The HTTP 1.0 spec already had a solution for two machines with different ideas of the current date. It’s one of my favorite parts of the spec and I’ve used it a few times in order to avoid having to implement my own time negotiation protocols (or in fact to stop others from doing it).
I don’t think that battery chemistry has changed all that dramatically since that time. It was still a 2032 cell, for machines that have a discrete battery. Instead it’s the clock chip and network time protocols that have gotten more efficient, and we use the machines more consistently. Or at least the machines where time counts matter the most are on all the time.