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As I understand it, the Leap Day trope is meant to apply to situations where the fact that February 29th happens only once every four years has some sort of plot significance. Despite this, Tropers are using it for any work which makes mention of leap days, which on its own probably falls under People Sit on Chairs. Additionally, there are numerous examples listed of characters who just so happen to have been born on a leap day, with no mention of how this impacts the story in any way.
Of the 53 examples on the trope page, there are 22 which are just birthdays that happen to fall on leap days, 14 birthdays which are significant because they are on a leap day, 9 significant leap days which do not involve birthdays, and 7 non-birthday leap days with no significance. In total, 23 examples of leap days significant to the plot, and 29 examples effectively stating "leap days exist".
It seems to me that the trope's name being just "Leap Day" is contributing to this misuse. The trope's name doesn't imply that there is any significance associated with the leap day, only that a leap day is involved in some capacity, no matter how incidental. While the quadrennial nature of leap days impacting the plot does seem trope-worthy, leap days existing does not. Because of this, I think changing the trope's name to reflect the significance of the leap day would be appropriate. Something along the lines of "Significant Leap Day", "Only on Leap Days", or "Leap Days Are Special" would almost certainly reduce ambiguity and misuse.
~That Fanwiththe Glasses, while it's nice that you checked the on-page examples, we're more concerned about the trope's use everywhere else. You can use a wick check for that.
Problem with only checking on-page examples is that the problem examples can easily be cleared away.
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