Why was Berlin the center of crisis in 1948-49 and again between 1958 and 1961?

Berlin was the center of crisis during these two time periods because of its history, its geographical location, and the geopolitical situation at the time.

To understand why crises arose over Berlin, we have to understand the geopolitics of the time mentioned in this question.  Both of these times were part of the Cold War era.  During the Cold War, the United States and the Soviet Union faced one another in a competition to dominate the world.  Each side wanted its ideology (democracy/capitalism for the US and communism for the USSR) to be the ideology that most countries on earth adhered to.  Each side distrusted the other and wanted to prevent the other from expanding.  The two main superpowers each had a variety of countries that were on their side in the conflict.  This conflict was the main fact about geopolitics during this era.

So what did Berlin have to do with this?  First, it was a historically important city.  It had been the capital of Germany and that country’s most important city.  Therefore, it was a major symbol of Germany and whoever controlled it would look like they dominated what had been Germany.  This brings us to a second historical fact.  After WWII, the victorious Allies divided Germany up into zones of occupation.  The Soviets controlled the eastern part of Germany while the French, British, and US each controlled part of the west.  The three western allies soon combined their zones and so there were two main zones of occupied Germany.

This is where geographical location came into play.  Berlin is located in eastern Germany.  Therefore, the city was within the Soviet zone of occupation.  However, because of its historical importance, the Allies split it up as well when they split Germany up. Thus, there was a part of the city, called West Berlin, that was democratic and capitalist in the middle of communist-controlled East Germany.  The Soviets wanted the US and its allies out of Berlin.  The US felt that it was important for them to have control of part of Berlin so they could be in control of at least part of Germany’s most important city.  Because the Soviets wanted the US out and the US was determined to stay, Berlin was the center of crisis both in 1948-9 (the Berlin Airlift) and 1958-61 (the Berlin Crisis that ended with the building of the Berlin Wall).