This is because on Motzaei Shabbat the revelation of Eliyahu begins, as our Sages teach: Eliyahu will come neither on Shabbat, nor on the eve of Shabbat (Eruvin 43b). Yet on Motzaei Shabbat he could come, and so the revelation of Eliyahu begins then.
Our Sages also teach: Eliyahu will come only to distance those who have drawn close through force, and draw close those who have been distanced through force (Ediyut 8:7). In other words, to distance that which is false, and draw close that which is true.
This is similar to what our Sages teach in the Zohar (II, 188a): A [Roman] official asked, “It is written (Proverbs 12:19), ‘The lip of truth shall be established’….” Rabbi Elazar answered, “It does not say ‘was established,’ but ‘shall be established.’ For the truth will in the future be established.” That is, when Eliyahu and the Messiah will come. See there.
When Eliyahu comes, and “in his day Yehudah and Yisrael will be saved” (Jeremiah 23:6), there will then be fulfilled: “the lip of truth shall be established.” He will distance those who until now drew close through force, which is falsehood, and he will draw close those who were distanced through force, for they correspond to the truth.
This is: “to distance those who have drawn close, and draw close those who have been distanced”—i.e., to distance that which is sheker (false), and draw close that which is emet (true). For our Sages have taught (Shabbat 104a): The letters of the word SheKeR are close, and the letters of the word EMeT are distant. Understand this.
Now, behold, Eliyahu will come to distance that which is false, corresponding to the Serpent, which is called “cursed” (Genesis 3:14). The Serpent brought death to the world, and sleep is one-sixtieth of death (Berakhot 57b). And since on Motzaei Shabbat the revelation of Eliyahu begins, falsehood, which is the Serpent, is banished. It is therefore difficult to sleep.
<In another vein,> our Sages teach: Ten measures of sleep descended into the world. Nine were taken by slaves (Kiddushin 49b). And “slave” is <Kanaan,> as in, “<Cursed is> Kanaan, the slave’s slave” (Genesis 9:25). <Thus, “slave”> corresponds to the Serpent, <for it, too, is “cursed”>.
Now, since Motzaei Shabbat is an aspect of the revelation of Eliyahu, and the aspect of Serpent—“Kanaan, the slave’s slave”—is banished, sleep, which descended for slaves, is banished. Therefore, ELiYaHU is numerically equivalent to BeN (son), the opposite aspect of slave.
Further: If there is no daat (holy knowledge), how can there be havdalah (separation)? (Yerushalmi, Berakhot 5:2). Thus, on Motzaei Shabbat, when there is Havdalah, there is an aspect of daat. For “if there is no daat ….” It is therefore difficult to fall asleep, because sleep is the absence of daat.
הָעִנְיָן שֶׁקָּשֶׁה לִישֹׁן בְּמוֹצָאֵי שַׁבָּת –
Regarding the matter of it being difficult to fall asleep on Motzaei Shabbat (Saturday night) <more so than on other nights:>
כִּי בְּמוֹצָאֵי שַׁבָּת מַתְחִיל הִתְגַּלּוּת אֵלִיָּהוּ, כְּמוֹ שֶׁאָמְרוּ חֲכָמֵינוּ זִכְרוֹנָם לִבְרָכָה (עירובין מג:), שֶׁאֵין אֵלִיָּהוּ בָּא בְּשַׁבָּת וְלֹא בְּעֶרֶב־שַׁבָּת, וּבְמוֹצָאֵי־שַׁבָּת יוּכַל לָבוֹא, וְעַל כֵּן מֵאָז מַתְחִיל הִתְגַּלּוּת אֵלִיָּהוּ.
This is because on Motzaei Shabbat the revelation of Eliyahu begins, as our Sages teach: Eliyahu will come neither on Shabbat, nor on the eve of Shabbat (Eruvin 43b). Yet on Motzaei Shabbat he could come, and so the revelation of Eliyahu begins then.
וְאָמְרוּ רַבּוֹתֵינוּ זִכְרוֹנָם לִבְרָכָה (עדיות פ"ח): אֵין אֵלִיָּהוּ בָּא אֶלָּא לְרַחֵק הַמְקֹרָבִין בִּזְרוֹעַ, וּלְקָרֵב הַמְרֻחָקִין בִּזְרוֹעַ; וְהַיְנוּ לְרַחֵק הַשֶּׁקֶר וּלְקָרֵב הָאֱמֶת.
Our Sages also teach: Eliyahu will come only to distance those who have drawn close through force, and draw close those who have been distanced through force (Ediyut 8:7). In other words, to distance that which is false, and draw close that which is true.
וּכְמוֹ שֶׁאָמְרוּ רַבּוֹתֵינוּ זִכְרוֹנָם לִבְרָכָה בַּזֹּהַר (תשא דף קפח), דְּשָׁאַל הַאי מִינָא: כְּתִיב: שְׂפַת אֱמֶת תִּכּוֹן וְכוּ', וְהֵשִׁיב לוֹ רַבִּי אֶלְעָזָר: כּוֹנַנְתָּ לֹא כְּתִיב אֶלָּא תִּכּוֹן, כִּי הָאֱמֶת עָתִיד לְהִתְקַיֵּם, דְּהַיְנוּ כְּשֶׁיָּבוֹא אֵלִיָּהוּ וּמָשִׁיחַ, עַיֵּן שָׁם.
This is similar to what our Sages teach in the Zohar (II, 188a): A [Roman] official asked, “It is written (Proverbs 12:19), ‘The lip of truth shall be established’….” Rabbi Elazar answered, “It does not say ‘was established,’ but ‘shall be established.’ For the truth will in the future be established.” That is, when Eliyahu and the Messiah will come. See there.
וְכַאֲשֶׁר יָבוֹא אֵלִיָּהוּ, וּבְיָמָיו יִוָּשַׁע יְהוּדָה וְיִשְׂרָאֵל, אֲזַי יְקֻיַּם: שְׂפַת אֱמֶת תִּכּוֹן; וִירַחֵק הַמְקֹרָבִין בִּזְרוֹעַ עַד עַכְשָׁו שֶׁהוּא בְּשֶׁקֶר, וִיקָרֵב הַמְרֻחָקִין בִּזְרוֹעַ, שֶׁהֵם בְּחִינַת אֱמֶת.
When Eliyahu comes, and “in his day Yehudah and Yisrael will be saved” (Jeremiah 23:6), there will then be fulfilled: “the lip of truth shall be established.” He will distance those who until now drew close through force, which is falsehood, and he will draw close those who were distanced through force, for they correspond to the truth.
וְזֶה: לְרַחֵק הַמְקֹרָבִין וּלְקָרֵב הַמְרֻחָקִין; הַיְנוּ לְרַחֵק הַשֶּׁקֶר וּלְקָרֵב הָאֱמֶת, כִּי אָמְרוּ רַבּוֹתֵינוּ זִכְרוֹנָם לִבְרָכָה (שבת קד): שֶׁקֶר מְקָרְבִין מִלֵּהּ וֶאֱמֶת מְרַחֲקִין מִלֵּהּ, וְהָבֵן.
This is: “to distance those who have drawn close, and draw close those who have been distanced”—i.e., to distance that which is sheker (false), and draw close that which is emet (true). For our Sages have taught (Shabbat 104a): The letters of the word SheKeR are close, and the letters of the word EMeT are distant. Understand this.
וְהִנֵּה אֵלִיָּהוּ יָבוֹא לְרַחֵק הַשֶּׁקֶר, שֶׁהוּא מִבְּחִינַת הַנָּחָשׁ, הַנִּקְרָא אָרוּר (בראשית ג), וְהַנָּחָשׁ הֵבִיא מִיתָה לָעוֹלָם, וְהַשֵּׁנָה הוּא אֶחָד מִשִּׁשִּׁים בְּמִיתָה (ברכות נז:). וְכֵיוָן שֶׁבְּמוֹצָאֵי־שַׁבָּת מַתְחִיל הִתְגַּלּוּת אֵלִיָּהוּ, נִדְחֶה הַשֶּׁקֶר, שֶׁהוּא הַנָּחָשׁ, לָכֵן קָשֶׁה לִישֹׁן.
Now, behold, Eliyahu will come to distance that which is false, corresponding to the Serpent, which is called “cursed” (Genesis 3:14). The Serpent brought death to the world, and sleep is one-sixtieth of death (Berakhot 57b). And since on Motzaei Shabbat the revelation of Eliyahu begins, falsehood, which is the Serpent, is banished. It is therefore difficult to sleep.
כִּי אָמְרוּ רַבּוֹתֵינוּ זִכְרוֹנָם לִבְרָכָה (קידושין מט:): עֲשָׂרָה קַבִּין שֵׁנָה יָרְדוּ לָעוֹלָם, תִּשְׁעָה נָטְלוּ עֲבָדִים. וְעֶבֶד הוּא בְּחִינַת (בראשית ט׳:כ״ה): כְּנַעַן עֶבֶד עֲבָדִים, וְהוּא בְּחִינַת אָרוּר (שם), בְּחִינַת הַנָּחָשׁ.
<In another vein,> our Sages teach: Ten measures of sleep descended into the world. Nine were taken by slaves (Kiddushin 49b). And “slave” is <Kanaan,> as in, “<Cursed is> Kanaan, the slave’s slave” (Genesis 9:25). <Thus, “slave”> corresponds to the Serpent, <for it, too, is “cursed”>.
וְכֵיוָן שֶׁבְּמוֹצָאֵי־שַׁבָּת הוּא בְּחִינַת הִתְגַּלּוּת אֵלִיָּהוּ, וְנִדְחֶה בְּחִינַת הַנָּחָשׁ, שֶׁהוּא בְּחִינַת כְּנַעַן עֶבֶד עֲבָדִים, נִדְחֶה הַשֵּׁנָה שֶׁיָּרְדָה לָעֲבָדִים. וְעַל כֵּן אֵלִיָּהוּ בְּגִימַטְרִיָּא בֵּן – הֶפֶךְ בְּחִינַת עֶבֶד:
Now, since Motzaei Shabbat is an aspect of the revelation of Eliyahu, and the aspect of Serpent—“Kanaan, the slave’s slave”—is banished, sleep, which descended for slaves, is banished. Therefore, ELiYaHU is numerically equivalent to BeN (son), the opposite aspect of slave.
וְעוֹד, כִּי אִם אֵין דַּעַת – הַבְדָּלָה מִנַּיִן (ירשלמי ברכות פ"ה). נִמְצָא שֶׁבְּמוֹצָאֵי שַׁבָּת שֶׁיֵּשׁ הַבְדָּלָה, הוּא בִּבְחִינַת דַּעַת, כִּי אִם אֵין דַּעַת וְכוּ'. וְעַל כֵּן קָשֶׁה לִישֹׁן, כִּי הַשֵּׁנָה הוּא הִסְתַּלְּקוּת הַדַּעַת:
Further: If there is no daat (holy knowledge), how can there be havdalah (separation)? (Yerushalmi, Berakhot 5:2). Thus, on Motzaei Shabbat, when there is Havdalah, there is an aspect of daat. For “if there is no daat ….” It is therefore difficult to fall asleep, because sleep is the absence of daat.