Clocks Are Too Precise
theatlantic.com
theatlantic.com
Programmers do not regularly write their own code to do so (and due to the hairy and brain numbing nature of it, plus that Java, Perl, Python, and Ruby all have good libraries to handle this anyways, no one wants to), and code almost always uses UNIX epoch time (number of seconds since the beginning of Jan 1st 1970 GMT) and does not observe leap seconds (as it is a linear progression of seconds, and does not have any concept of minutes or higher).
Perhaps the fragility of these systems is more of a problem than the leap-second?