Computers are continuously being time corrected — and restarted/recreated
Maybe MS-Windows computers are, but real computers can run for a long time without being restarted.
That said, worrying about leap seconds is a waste of time. Critical software should be designed to deal with the very occasional 61 or 58 second minutes. When you hit one, you can have a process look up and validate leap-seconds.list if it's important to you.