The Midrash continues on and relates that the great Tana, Rabbi Akivah, was once teaching his talmidim when, at one point, the audience began dosing off. To awaken them, he raised the following query: why did Esther Hamalkah merit to rule over a hundred and twenty-seven countries? The reason is, he continued, that it was due to Sarah Imeinu who lived for the same number of years. Thus, Hashem said that Esther, a descendant of Sarah, would rule over one hundred and twenty-seven countries, each country corresponding to one year of Sarah Imeinu's life.
The Chasam Sofer explains this Midrash with an idea that is similar to the concept mentioned above.
He also questions, how it is possible that Esther was rewarded for the full 127 years of her life. How can she be rewarded equally for her childhood years as for the rest of her life? Can a child a of one or two years merit any reward for her actions?
To solve this, the Chasam Sofer first clarifies a possuk in the chapter of Eishes Chayil, as Chazal (מדרש תנחומא פ"ד) teach us that this chapter (which is customarily sung in Yidishe homes on Friday Nights) is the eulogy that Avraham delivered for his wife Sarah. The possuk states וַתָּקָם בְּעוֹד לַיְלָה וַתִּתֵּן טֶרֶף לְבֵיתָהּ וְחֹק לְנַעֲרֹתֶיהָ - she rises when it is still night; she gives food to her household and an allotted share to her maidens (משלי לא טו). The words וְחֹק לְנַעֲרֹתֶיהָ seem superfluous. What is there to add to when the possuk already says that she feeds her household?
The answer to this, says the Chasam Sofer, is that through her extra efforts in her later years, Sarah 'made up' for her earlier years. Therefore, all her years are counted as equally fulfilled; she completed a full 127 years filled with mitzvos and maasim tovim.
This is hinted in the possuk וַתָּקָם בְּעוֹד לַיְלָה - she, Sarah arose (early) when it was still night. And with this added investment she 'fed' all her years with avodas Hashem, gaining extra reward for her entire life - including those early years - which was later granted to her descendant Esther, in the form of 127 countries. That's why the possuk continues וַתִּתֵּן טֶרֶף... וְחֹק לְנַעֲרֹתֶיהָ - a reference to Esther Hamlkah; it was Sarah Imeinu's early rising which enabled her to obtain this great monarchy for Esther.
With this, the Tana Rabbi Akiva aimed to awaken his audience. He was implying to his talmidim that by allowing themselves to be overcome by sleep during the day, they were achieving the exact opposite of our Matriarch Sarah.
(חתם סופר עה"ת ד"ה במ"ר ר"ע)