Are you asking why Israeli forces were unable to capture all of Jerusalem in the 1948 war?

It's a complicated question, because there are both political and military answers. The TL,DR of it is that Israel and Transjordan had a tacit agreement to subdivide the Palestinian territories, but reached a stalemate situation in Jerusalem with Israeli forces unable to drive out King Abdallah's well led Arab Legion.

Militarily, what we now would call the West Bank and East Jerusalem was conquered and occupied by the Arab Legion. The Arab Legion was the army of King Abdullah of Transjordan, the British protectorate that in 1949 would be renamed Jordan.

Significantly, the Arab Legion was trained and commanded by British officers. Compared to other Arab military forces of the time, it was well equipped and organized. During the 1948-1949 war, it certainly had more battlefield victories against Israeli forces than any other Arab military.

Politically, King Abdullah had fairly extensive negotiations with Zionist leaders in the months leading up to end of the British Mandate. King Abdallah's position was tenuous and his state was poor. He did not want to risk serious damage to his small but well trained army.

He made it clear to the Yishuv that he did not seek war with Israel but wanted control of the West Bank territories that were supposed to be assigned to a Palestinian state. A tacit agreement was reached that Transjordan would seize the West Bank region but not directly invade Jewish assigned territories after partition. In effect, Abdullah agreed to divide Arab Palestine with the Jewish state. The status of Jerusalem was not clearly decided upon.

Upon formal outbreak of hostilities, the Arab Legion, still led by British officers, crossed into the West Bank and settled into well fortified positions at Latrun, dominating the Tel Aviv - Jerusalem road. They did not attempt to drive further on to the Jewish settlements on the Mediterranean coast, and, indeed, had no plans to do so despite being in a formal state of war with Israel. Their objective was to take territory for Transjordan, not to attack and defeat the Jewish state.

There was nevertheless extensive fighting around Jerusalem and along the road from Tel Aviv to Jerusalem. After some initial Israeli successes against Palestinians in the Jerusalem area, the Arab Legion was ordered to occupy East Jerusalem and the old city. The 100,000 Jewish residents of Jerusalem required supplies from the coast, the trucks containing which came under regular attack by Palestinian irregular forces.

In the first few months of the 1948 war, Israel suffered heavy casualties failing to dislodge the Arab Legion from their fortifications at Latrun but succeeded in setting up a bypass road to supply their civilians and armed forces in Jerusalem. Arab forces took most of East Jerusalem including the old city, but did not seize Jewish controlled west Jerusalem neighborhoods, and did not have a serious plan to do so.

Having succeeded in taking most of the West Bank, Abdullah had no desire to wage further hostilities. The Arab Legion settled down to what its British commander would later describe as a "phony war", and Israel devoted itself to defeating in detail the expeditionary forces of Egypt and Syria. Jerusalem remained relatively quiet.

At the close of the 1948 war, King Abdullah was easily the Arab leader who had benefited the most. He had occupied the West Bank and the holy sites of Jerusalem without taking significant damages to his army.

Source: Benny Morris. The road to Jerusalem: Glubb Pasha, Palestine and the Jews. 2002.