It is the accepted practice that the Tallit, through which the commandment of wearing Tzitzit is fulfilled, is worn only during the morning prayers, also known as Shacharit. Why?
In the book of Genesis, in the section called Lech Lecha a story is related regarding Abraham. Abraham (at the time of the story was called Abram, only later G-d added on the extension making his name Abraham) had rescued his nephew Lot and the king of Sedom from the hands of five other kings.
The king of Sedom turns to Abraham in gratitude and offers Abraham spoils of war. Abraham is then quoted as saying, “I have raised my hands to Hashem, G-d the most High, Maker of heaven and earth. If so much as a thread or a shoe strap; or if I shall take from anything that is yours so you shall not say, “It is I who made Abraham rich” (Genesis 14:22, 23).
Abraham had no problem in the previous verse accepting tithes from Avimelech the king of Shalem. Seemingly, there was something in the wickedness of the people of Sedom that Abraham realized that even the acceptance of a mere shoelace could ruin him. He did not want to be associated in any way whatsoever with the people of Sedom.
The Talmud (Sotah 17a) informs us that as a reward for Abraham’s refusal to accept even a thread of shoe strap his children merited two commandments; the blue thread, also known as Techelet, in the Tzitzit and the strap of Tefillin.
This is a classic example of the concept of “All of G-d’s traits are measure for measure” which appears in the Talmud and Mishnah. Essentially, it means that G-d treats people in the same way they treat others. Abraham had correctly refused to accept even a thread or shoelace from the Sedomite people and measure-for-measure G-d rewards him with two commandments that correspond to the thread and shoelace.
The Jewish Sages taught that the three daily prayers- Shacharit (morning prayers), Mincha (afternoon prayers) and Aravit (Evening prayers) were instituted by the three Patriarchs. Abraham was the first to say Shacharit; Yitzchak established Mincha and Jacob, Aravit.
This therefore explains why the Tallit is only worn in morning prayers. The commandment to wear Tzitzit was given in Abraham’s merit and we therefore wear the Tallit specifically in “his” prayer of Shacharit.
Based on essay by Rabbi Baruch S. Davidson.