Rabbi Debra Orenstein taught, during her many High Holy Days as rabbi of Makom Ohr Shalom, that the gates of repentance do not completely close at the conclusion of Yom Kippur. Instead, a crack remains open to allow us to complete teshuvah by Sukkot or Simchat Torah.... or even until the end of Hanukah.*
Perhaps, if we do embrace my proposal for blowing shofar on Hanukah, it can also serve as the Tekiah Gedolah for the final end of the repentance season.
* According a reply to a question I sent to www.askmoses.com, "There are different sources given for this from disciples of Rabbi Israel Baal Shem Tov. For a complete list of sources, please see Nitei Gavriel on Chanukah chapter 56 footnote 1." If you have access to this reference or know another source for her teaching, please add a comment below.