We are told why Moshe and Aharon passed away in the desert (Bamidbar 20:12), but we are not told why Miriam died.
According to Rashi (Bamidbar 1:49, 26:64), only the men who were counted in the primary census died in the desert. Does this not indicate that no women died in the desert? If that's the case, Miriam was the only one. Why?
[See here where it is suggested that Miriam died through no fault of her own, rather to teach us that death is beyond human understanding]
Chumash Torah Sheleima (Bamidbar 20:1) brings the Midrash Esfah that says as follows (Free translation):
And Miriam Died There: She alone died from all the women that left Egypt, since the women did not die in the desert. As it is stated (Yehoshua 5:4) "All the people that came out of Egypt, that were males, all the men of war, had died", but not the women.
And why did she (i.e. Miriam) die? Because of the well that was given because of her. It was not possible that the she should still be around and the well that was in her honor would depart.
Another answer, because she was equal in greatness to Moshe and Aharon, as all 3 were the "good providers of the Jews" (Talmud Taanit 9A), and it was not just (proper) that they (Moshe and Aharon) should pass away while Miriam remained. Therefore she passed away first.
The Kli Yakar (Bamidbar 20:4), while not addressing the question, says that Miriam dies so that the well that was in her merit would stop flowing. This is because there were people in Kadesh who didn't want to enter the land and once they water stopped they realized they couldn't stay there.
On the pasuk (Bamidbar 20:1) וַיָּבֹ֣אוּ בְנֵֽי־יִ֠שְׂרָאֵל כָּל־הָ֨עֵדָ֤ה מִדְבַּר־צִן֙ בַּחֹ֣דֶשׁ הָֽרִאשׁ֔וֹן וַיֵּ֥שֶׁב הָעָ֖ם בְּקָדֵ֑שׁ וַתָּ֤מָת שָׁם֙ מִרְיָ֔ם וַתִּקָּבֵ֖ר שָֽׁם׃: The Bnei Yisrael, the whole congregation, arrived at the wilderness of Zin in the first month, and the people stayed at Kadesh. And Miriam died there and she was buried there.
Rashi writes:
כל העדה= עֵדָה הַשְּׁלֵמָה, שֶׁכְּבָר מֵתוּ מֵתֵי מִדְבָּר וְאֵלּוּ פֵרְשׁוּ לַחַיִּים: - כל העדה , the WHOLE congregation — The congregation in its entirety, for those who were to die in the wilderness in consequence of their sin had already died, but these had been expressly mentioned for life.
ותמת שם מרים. לָמָּה נִסְמְכָה פָרָשַׁת מִיתַת מִרְיָם לְפָרָשַׁת פָּרָה אֲדֻמָּה? לוֹמַר לָךְ, מַה קָּרְבָּנוֹת מְכַפְּרִין, אַף מִיתַת צַדִּיקִים מְכַפֶּרֶת (מועד קטן כ"ח):
AND MIRIAM DIED THERE — Why is the section narrating the death of Miriam placed immediately after the section treating of the red cow? To suggest to you the following comparison: What is the purpose of the sacrifices? They effect atonement! So, too, does the death of the righteous effect atonement! (Moed Katan 28a).
The Chasam Sofer explains the connection between these two psukim:
ונ"ל בטעם מיתת מרים לכפר על העדה אחר שכבר מתו מרגלים וכל העדה שלמים ליכנס לא"י עכ"פ הוצרכו כפרה שיהיו ראויים ליכנס ומתה הצדקת לכפר על עון העדה, ומעתה אחר מיתת הצדקת הי' כולם מהנאמר ואתם הדבקים חיים כולכם היום.
It seems to me, that the reason for the passing of Miriam was to bring attonement on the people, since the [people who were involved in the sin of the] spies had already died, and the rest of the congregation was wholesome [and] ready to enter Eretz Yisrael, they nevertheless needed [extra] attonement in order to be able to enter, and thus, the tzdekes (righteous woman) Miriam passed away to [completely] attone for the sin of the congregation, and now after the death of the tzadekes, they were all of those about which the pasuk says וְאַתֶּם הַדְּבֵקִים בהוי"ה אֱלֹהֵיכֶם חַיִּים כֻּלְּכֶם הַיּוֹם. (Devarim 4:4) [But you who cleave to the L-rd your G-d are alive, all of you, this day].
