Rabbi Nachman of Breslov taught that the root cause of exile is a lack of faith. And the cure for exile is the Land of Israel.
The connection is not sentimental. It is structural. Faith, prayer, and miracles are three aspects of the same reality. Prayer transcends nature because it changes what the natural course would otherwise produce. That is, by definition, a miracle. And miracles require faith, the belief that there exists an Originator with the power to override nature at will.
The Land of Israel is where all three converge. "Dwell in the Land and cultivate faith" (Psalms 37:3). The principal elevation of prayer happens there: "This is the gate of heaven" (Genesis 28:17). The Land itself "drinks first" from the primordial depths (Taanit 10a), from a source so wondrous that the Talmud connects it to the word tehomah, amazement.
Rabbi Nachman traces the first exile directly to a crisis of faith. When Abraham asked God, "How shall I know that I will inherit it?" (Genesis 15:8), he blemished the very connection between faith, prayer, and the Land. The result was the exile in Egypt. And it was specifically Jacob and his twelve sons who descended, because they correspond to the twelve versions of prayer described in the Zohar (III:170a).
Egypt is the opposite of the Land of Israel. Egypt is not the place of miracles, and the Egyptians were "fleeing against" the miraculous (Exodus 14:27). It is not the place of prayer: "When I go outside the city I will spread out my hands" (Exodus 9:29), implying that within the city of Egypt, prayer could not function properly.
All exiles are called Mitzrayim (מצרים), because they cause anguish (Bereishit Rabbah 16:4). When a person damages their faith, their connection to prayer and miracles, they fall into a personal Egypt. The Messiah will come, the Talmud says, when the last penny of faithlessness is spent (Sanhedrin 97a).