The articles touches on this second being added is a problem for systems not designed to handle it. They cite Amazon, Yelp, etc. Why is this an obstacle for sy

The articles touches on this second being added is a problem for systems not designed to handle it. They cite Amazon, Yelp, etc. Why is this an obstacle for systems? I get that it would mean that your system is one second off the atomic clock, but if you sync with a time server wont't this remedy itself if the time server was updated, if it fell behind?