The Gemara (Megillah 4) states, "A person must read the megillah at night and repeat it in the daytime."
The source for this is the pasuk (Tehillim 22:3) לי דומיה ולא ולילה תענה ולא יומם אקרא אלקי, 'Hashem, I call out by day, and You do not reply, and at night I do not keep silent.'" This alludes to the Yidden's tefillos at that time.
But there is a great question. This pasuk discusses times when our tefillos are not answered! Shouldn’t the pasuk alluding to the miracle of Purim discuss times when our tefillos were answered? Also, let's look at a pasuk before it (which also discusses the story of Purim). It states (22:2) לי"א עזבתני למה לי"א, "My G-d, my G-d, why have You forsaken me?" Once again, is this an accurate description of the miracles of Purim?
However, further in this chapter, there are many references to Hashem answering our tefillos. For example, (22:25) שקץ ולא בזה לא כי עני ענות, "For He neither despised nor loathed the prayers of the poor..."
This is because tefillah is a process. It isn't that we daven and are answered immediately. Each tefillah brings the salvation closer. Sometimes, we have to offer many tefillos before our requests are granted. The chapter discusses the two stages of tefillah: The first stage is when we daven and don't see results, and the second stage is when Hashem sends us our yeshuah.
We can also explain the chapter b'derech tzachus: After Purim passes, people often feel joyful that they had the opportunity to do so many mitzvos and daven to Hashem on this special day. But, simultaneously, they say, "I wish Purim would be longer; I would do so much more!"
It can be compared to someone who walked through a desert and found a mountain of diamonds. He fills all his pockets with precious stones (as well as his fists, socks, and shoes) and rejoices with his good fortune. But as he walks away from this unique mountain, he thinks, "I wish I had more pockets..."
This is hinted at in this chapter. It mentions our tefillos that were answered and addresses our requests that weren't answered. It is implying, "Baruch Hashem for what we grasped. If only Purim were longer, we could have gained so much more!"
