Despite its great virtue, the Chachamim did not establish Nefillat Apayim to be an obligatory prayer, and they did not institute a set wording for it. Anyone who so desired would add prayers of supplication in prostration after reciting the Amidah. Perhaps specifically because of its superior value, being that it expresses total submission to the Creator, May He Be Blessed, it is befitting that it emanates from the heart, from one’s most inner resolve.
During the period of the Geonim, a permanent wording for Nefillat Apayim, and the prayers of supplication after the Amidah, began to take shape. In the time of the Rishonim, the wording became established, until all Jews accepted upon themselves the obligation to recite certain specific supplications. Seemingly, as a result of the suffering of the Diaspora, which continued to intensify, our hearts were dulled. This necessitated the introduction of a permanent wording of supplication. Because the nusach of the supplications became widespread only after the scattering of the exiles, the differences between the Sephardic and Ashkenazic wordings are more pronounced.
The Nefillat Apayim prayer expresses heartbreak, manifested by the submission of one’s body and sacrifice of one’s soul. Therefore, it is not recited on holidays, or days of joy due to the celebration of a special mitzvah like a brit milah. The kabbalists explain that all the tikkunim (rectifications) performed on regular days via the Nefillat Apayim prayer are achieved on days of a mitzvah celebration purely through the joyous sanctity of the day (Kaf HaChaim 131:54). Additionally, when those celebrating such a joyous mitzvah are present in the synagogue, prayers of supplication are not recited (as explained in halachot 7 and 8). We have already learned that, in principle, there is no obligation to recite Tachanun, and therefore in any situation in which there is doubt as to whether Tachanun should be said, the instruction is not to recite it.
Similarly, in a house of mourning, it is customary not to recite Tachanun, since the Divine attribute of judgment (midat hadin) is present there, and care should be taken not to amplify it (Mishnah Berurah 131:20). The idea behind this is that the person praying Nefillat Apayim demonstrates to himself that his existence is dependent on Hashem, and that he is null and void in relation to Him. Since a mourner already has an acute sense of this, it is unnecessary to add to it.