The Halachic obligation to celebrate the day of a miracle
A day in which a miracle occurred is to be commemorated throughout the generations. This celebration is not a mere matter of thanks but according to some Poskim carries with it a Biblical obligation. There are laws and customs associated with this day of celebration such as making meals and omitting Tachanun.
1. The Biblical obligation to commemorate the day:
All holidays instituted to commemorate a miracle of G-d have Biblical status, and hence the commemoration of Chanukah and Purim are of Biblical origin. Nevertheless, even according to this opinion, the form of how to commemorate the miracle is only Rabbinical, and hence the lighting of the candles, and other matters involved in the form of commemoration, are Rabbinical according to all. Nevertheless, even these Rabbinical forms of commemoration are of Biblical origin, as the Torah commands one to adhere to the words of the Sages and not swerve from their words. [Accordingly, the celebration of Yud Tes Kisleiv which celebrates a miracle that Hashem performed for the Alter Rebbe and the entire Chassidic movement, and continuity of Chasisdus, has Biblical status, and fulfills a Biblical Mitzvah.]
2. Making a meal of commemoration-Seudas Hodaya:
It is customary to celebrate a miracle through making a festive meal for one’s friends and family. During this meal one recounts the miracle that occurred and gives thanks to Hashem for His great kindness. [The Alter Rebbe celebrated a Seudas Hodaya for his release from imprisonment of Yud Tes Kisleiv on the 19th of Kisleiv 1801/5561, two years after his release from prison. The Alter Rebbe treated this meal as an absolute obligation, and a Halachic discussion ensued with his brother the Maharil regarding what one is to do if he did not make the Seudas Hodaah on time.]
Seudas Mitzvah: A meal that takes place to commemorate a miracle performed by Hashem is considered a Seudas Mitzvah.
3. Not to say Tachanun:
It is customary not to say Tachanun on the day which one celebrates the miracle that took place. [For this reason Tachanun is not recited on Yud Tes-Chaf Kisleiv.]
 Chasam Sofer Yoreh Deah 233
 However if one passes the Holiday without performing any form of commemoration of the miracle then he has transgressed a Biblical command according to this opinion. [ibid]
 Shabbos 23a; Admur 158/16
 Shelah; Chavos Yair 70; P”M 444 M”Z 9; Chayeh Adam 155/42; Shulchan Hatahor 219/7; Soles Belula 218/2; Kaf Hachaim 218/9
 I have not found any source in Poskim for this meal being obligatory, and on the contrary the above Poskim all write it is a mere custom. However from the Sefer Hasichos below it is implied that it is an obligation.
 Sefer Hasichos 1940 p. 54-58 [Hebrew], retold by the Rebbe Rayatz in name of Rav Issac Homlir.
 Chavos Yair 70; P”M 444 M”Z 9; Chayeh Adam 154/42 in name of Rashal Baba Kama 37; M”B 697/2
Other Poskim: Some Poskim rule that a Seudas Hodaya is not considered a Seudas Mitzvah. [Peri Chadash 496]
 Lev Chaim 150; Kaf Hachaim 218/9; Tzitzis Eliezer 10/10
 See Ketzos Hashulchan 24 footnote 30