http://revach.net/article.php?id=4420

Section: Moadim   Category: Megilas Esther
Megilas Esther: Which Day Did The Yehudim Go Hungry At Achashveirosh's Party?
"Aivel Gadol LaYehudim V'Tzom U'Vchi U'Misped Sak VaEifer" (Esther 4:3).  When the Bnei Yisroel received word of their decreed annihilation they repented in the six ways mentioned in the Pasuk.  They mourned and fasted, cried and lamented, and donned sack-clothes and ashes.  The Rokeach says that these six things were a tikun for the six days they enjoyed Achashveirosh's feast.  What about the seventh say since it clearly says the party for Shushan was a seven day event?

The HaMeor SheBiMegila brings from the Yeshua Gedola as follows.  The Rokeach says that the 180 day party that Achashveirosh threw was during the summer months.  He knows this because after already telling us the party was 180 days, the Megila says again "Yamim Rabim".  Therefore this must means not many days but long days, or the days of the summer which are long.

Nisan through Tishrei is 177 days so the party ended on 3 Tishrei.  The Shushan party started the next day, and the seventh day was Yom Kippur.  Surely the Yehudim did not eat at the party on Yom Kippur so they only needed to do tshuva for six of the days and not all seven.