5
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(with apologies to @Rand al'Thor, whose latest puzzle inspired me to post this one, my first here—and whose text I blatantly stole lovingly adapted in homage.)

I came regularly once a year, from '92 to '95,
Skipped 1996 entirely,
Returned in 1997, and took a break after 1998.
I made a few appearances between '05 and '13,
But in '15 I was back like clockwork.
This year I haven't appeared at all!

Who am I? And when will I next appear?

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    $\begingroup$ this happened literally once in each year where it happened. $\endgroup$ – Rubio Oct 28 '16 at 16:12
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    $\begingroup$ It looks to be almost a leap second, but that doesn't fit with regularly once a year, from '92 to '95 because the first 3 of those were on Jun 30, but in 1995 the leap second was added on Dec 31. $\endgroup$ – FumbleFingers Oct 28 '16 at 18:07
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    $\begingroup$ actually 11:59:60 pm UTC, or 23:59:60 UTC. I'll point out here that the title of this riddle is no accident. anyone gonna actually make an answer out of all this yet? hehe $\endgroup$ – Rubio Oct 29 '16 at 6:27
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    $\begingroup$ I just came here to make that remark about the title but Rubio had got there first :-). @FumbleFingers should do it and get all that lovely lovely rep. $\endgroup$ – Gareth McCaughan Oct 29 '16 at 10:04
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    $\begingroup$ @FumbleFingers I left the word regularly in as once per year is indeed regular - and because the puzzle I was intentionally mirroring used the word there (and in a similar inexact sense). Spelling out a puzzle with zero ambiguities is possible, sure, but I think leaving something that needs to be puzzled over how it might fit is part of the fun. In any case you were the first (and maybe only) one to hit on the right answer, which I would have loved to give you due credit for - well done, and I hope you stick around Puzzling :) $\endgroup$ – Rubio Oct 29 '16 at 17:38
1
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This is from a comment by FumbleFingers, who should feel free to make a separate answer and get full credit.


           (source Wikipedia)

Who am I?

A leap second

          Last seen:
(from Wikipedia)

And when will I next appear?

Saturday

December 31, 2016, at 23:59:60 UTC

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