http://revach.net/article.php?id=4478

Section: Moadim   Category: Hagadah Shel Pesach
Amar Rebbi Elazar -Why Was Rebbi Elazar Ben Azarya Up All Night?
Right in middle of the Hagadah we say the Mishna discussing Rebbi Elazar Ben Azarya's shitta that Yetzias Mitzrayim is a mitzva every night as well as by day.  What does this have to do with the Hagadah, and why now?

The Otzeir Divrei Meforshim brings the Smicha LaChaim who answers this question with another question.  Rebbi Elazar Ben Azarya held that the mitzva of Korban Pesach is only until Chatzos.  Therefore according to Rebbi Elazar Ben Azarya the mitzva of V'Higadita L'Bincha, to retell your children the story of Yetzias Mitzrayim, is also only until Chatzos.  If so in the previous paragraph in the hagadah why was he awake the entire night until Zman Krias Shema with the other Tana'im in Bnei Brak, if there was no mitzva.

To answer this, the Ba'al Hagadah tells us that although the Mitzva of V'Higadita is not after chatzos, Rebbi Elazar Ben Azarya held that there is a mitzva of Zechiras Yetzias Mitzrayim every night of the year.  This mitzva is during the entire night even after chatzos.  That is why Rebbi Elazar Ben Azarya stayed around all night with his colleagues.