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Scientists just voted to redefine how the world keeps time
(www.scientificamerican.com)
This is a most excellent place for technology news and articles.
https://gist.github.com/timvisee/fcda9bbdff88d45cc9061606b4b923ca
If your software is choking on completely expectable events, it it not sufficiently robust.
As you just proved, while it might be possible to write robust software that deals with dates/times, I wouldn't bet on it, and it's Definitely not practical to try.
But you are right that leap seconds were common enough to try and handle. There's a bunch of ways to handle them though, each incompatible with the others.