An unbirthday (originally written un-birthday) is an event celebrated on all days of the year which are not a person's birthday.
[1][2] The concept gave rise to "The Unbirthday Song" in the 1951 animated feature film Alice in Wonderland.
[3] In Through the Looking-Glass, Humpty Dumpty is wearing a cravat (which Alice at first mistakes for a belt) which he says was given to him as an "un-birthday present" by the White King and Queen.
[4] In the Disney animated film Alice in Wonderland, Alice stumbles upon the Mad Hatter, the March Hare and the Dormouse having an unbirthday party and singing "The Unbirthday Song" (music and lyrics by Mack David, Al Hoffman and Jerry Livingston).
The scene from the film combines the idea of an unbirthday introduced in Through the Looking-Glass with the "Mad Tea Party" described in Alice's Adventures in Wonderland.