According to my Nusach Ashkenaz Siddur, the Thirteen Middos are preceded by a passage beginning קל ארך אפים, whose text is as follows:

אֵ-ל אֶרֶךְ אַפַּיִם אַתָּה וּבַעַל הָרַחֲמִים נִקְרֵאתָ. וְדֶרֶךְ תְּשׁוּבָה הורֵיתָ. גְּדֻלַּת רַחֲמֶיךָ וַחֲסָדֶיךָ תִּזְכּור הַיּום וּבְכָל יום לְזֶרַע יְדִידֶיךָ. תֵּפֶן אֵלֵינוּ בְּרַחֲמִים. כִּי אַתָּה הוּא בַּעַל הָרַחֲמִים. בְּתַחֲנוּן וּבִתְפִלָּה פָּנֶיךָ נְקַדֵּם. כְּהודַעְתָּ לֶעָנָו מִקֶּדֶם. מֵחֲרון אַפְּךָ שׁוּב. כְּמו בְּתורָתְךָ כָּתוּב. וּבְצֵל כְּנָפֶיךָ נֶחְסֶה וְנִתְלונָן. כְּיום וַיֵּרֶד ה' בֶּעָנָן. תַּעֲבר עַל פֶּשַׁע וְתִמְחֶה אָשָׁם. כְּיום וַיִּתְיַצֵּב עִמּו שָׁם. תַּאֲזִין שַׁוְעָתֵנוּ וְתַקְשִׁיב מֶנּוּ מַאֲמַר. כְּיום וַיִּקְרָא בְשֵׁם ה' וְשָׁם נֶאֱמַר:

My Nusach Ashkenaz Selichos for fast days and Elul/Tishrei include this passage for the first time the Middos are said, while the following one is inserted each subsequent time:

אֵ-ל מֶלֶךְ יוֹשֵׁב עַל כִּסֵּא רַחֲמִים מִתְנַהֵג בַּחֲסִידוּת, מוֹחֵל עֲוֹנוֹת עַמּוֹ מַעֲבִיר רִאשׁוֹן רִאשׁוֹן, מַרְבֶּה מְחִילָה לְחַטָּאִים וּסְלִיחָה לַפּוֹשְׁעִים, עֹשֶׂה צְדָקוֹת עִם כָּל בָּשָׂר וָרוּחַ, לֹא כְרָעָתָם תִּגְמוֹל, אֵ-ל הוֹרֵיתָ לָּנוּ לוֹמַר שְׁלֹשׁ עֶשְׂרֵה, וּזְכָר לָנוּ הַיּוֹם בְּרִית שְׁלשׁ עֶשְׂרֵה, כְּהוֹדַעְתָּ לֶעָנָיו מִקֶּדֶם, כְּמוֹ שֶׁכָּתוּב וַיֵּרֶד ה׳ בֶּעָנָן וַיִּתְיַצֵּב עִמּוֹ שָׁם, וַיִּקְרָא בְשֵׁם ה׳:

My Nusach Ashkenaz Machzor for Yom Kippur includes this latter paragraph every time they’re mentioned. Why? Why isn’t the former paragraph mentioned the first time the Middos are recited during Selichos after Maariv and during Ne’ilah, the same way that they are during Selichos on other days?

  • Your Nusach Ashkenaz Machzor is apparently missing most of Selichot for Yom Kippur (such as those for Shacharit Musaf and Mincha). It's not surprising that this part, which is part of the uniform introduction to all 5 sets of Selichot, was omitted too along with the standard opening line סלח לנו אבינו כי ברוב אולתינו שגינו... – Double AA Oct 8 at 21:41
  • @DoubleAA Do you have a link to a Machzor which includes it? If it helps for reference, mine begins at Maariv with Ya’aleh Tachanuneinu, the usual Shome’ia Tefillah said during Selichos, and a few individual lines to say responsively (beginning darkecha, lema’ancha, and ta’aleh) before the first recital of the י״ג מידות; and at Ne’ilah, just a few individual lines (beginning pesach, hayom yifneh, and ana Keil na) before the first recital. Are all of my questions I’ve been asking answerable with “because ArtScroll”?! (I should clarify that I have piyutim during the others, just not Selichos.) – DonielF Oct 8 at 21:47
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    judaism.stackexchange.com/questions/95520/… I used Bloch's for the first time this year and enjoyed. It was [allegedly?] the standard Machzor in America 75 years ago. (I don't remember if that particular Machzor had the specific variant I proposed above) – Double AA Oct 8 at 21:53
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    Ok it has Kel Erekh Apayim Attah before the Slichot for Shacharit Musaf and Mincha, but I can't find it anywhere before Maariv and only one reference to before Neilah. It must have been commonly forgotten earlier than the rest of Slichot were generally forgotten. I'm convinced though I'll find it if I look somewhere old enough. Neilah is traditionally one of the shorter Slichot sets because of the time crunch. Maariv too is at night and there's a darkness factor. I bet that's why people trimmed them first. I'm not sure this is technically an answer though. – Double AA Oct 8 at 22:31
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    On the contrary, putting it in the back isnt appropriate at all. They should include it up front and everything else in the back so that people resume the practice of their grandparents and all Jewish communities over millennia to say the MOST IMPORTANT parts of Yom Kippur communal prayers: Slichot. The current situation of spending most of the day reciting non Slichot Kedushtot is as embarrassing as it is ridiculous. Complete Minhag Taut. Against all Rishonim. No classical support. – Double AA Oct 8 at 22:39

Nit'ei Gavriel, Rosh HaShanah ch.2 fn. 33 explains that in general we switch from keil erech apayim to keil melech yosheiv after the first recitation of the thirteen middot. This is because after the first recitation of the middot, G-d (so-to-speak) moved from His Throne of Judgement to His Throne of Mercy. So after we have said the thirteen middot once (introduced by keil erech apayim) we can subsequently say keil melech yosheiv al kisei rachamim.

On Yom Kippur, which is a day of complete mercy, we can say keil melech yosheiv al kisei rachamim from the very beginning, without having to have said the thirteen middot first. Thus, there is no need to say keil erech apayim at all on Yom Kippur.

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    I note from comments to the OP that this is very possibly only a justification for the current common custom, and that older customs would indeed have recited keil erech apayim on yom kippur as well. – Joel K Oct 9 at 8:25

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