Many classic sources tell us that Purim represents a special opportunity for one’s prayers to be answered.
The Sefer Kav HaYosher says the following: Taanis Esther is a day that is very auspicious for one’s prayers to be answered in the merit of Mordechai and Esther. Whoever needs mercy for any particular needs should put aside time for themselves and do the following: First, recite Chapter 22 in Tehilim. Then, pour out your heart to Hashem and ask for all your needs and mention the merit of Mordechai and Esther [whose merits saved us from Haman]. The Gates of Mercy will be opened and your prayers will be accepted beratzon.
More segulot for Purim at Zchus Avos
The Ritv”a in his commentary to Megillah 7a quotes the Talmud Yerushalmi which explains regarding the fulfillment of the obligation to give matanos la’evyonim [gifts to the poor] on Purim, that kol ha’posheit yado leetol yitnu lo - we give to anyone who extends his hand to receive”. This is to say that on this festive day we give money to everyone who asks, without first checking to see if they truly are poor and worthy of receiving tzedakah funds. The Chasam Sofer writes that just as we are not particular if the people to whom we give charity on Purim are truly deserving, and whoever extends his hand gets helped, so, too, does G-d listen to all our prayers on this special day, and kol ha’posheit yado leetol yitnu lo – He gives to anyone who extends his hand to receive.
Also see: Purim's Golden Opportunity