Been reading about this on wikipedia and it says this:
The continued success of the Airlift humiliated the Soviets, and the "Easter Parade" of 1949 was the last straw. On 15 April 1949 the Russian news agency TASS reported a willingness by the Soviets to lift the blockade. The next day the US State Department stated the "way appears clear" for the blockade to end. Soon afterwards, the four powers began serious negotiations, and a settlement was reached, on Western terms. On 4 May 1949 the Allies announced an agreement to end the blockade in eight days' time.
I understand that the Soviets failed to enforce the blockade, but why would they agree to lift it on Western terms? As I understand it, Stalin was a pretty hard man and even though the West could indefinitely supply West Berlin using aircraft, they were incurring a substantial expense in doing so.
What was the cost to the soviets to maintain the blockade that they felt compelled to lift it?
The heart of the answer lies in the reason for the blockade in the first place. Stalin had hoped that he could force the entirety of Berlin into Soviet control through the blockade. By February 1949 it was pretty clear to the Soviets that this strategy had failed. This is when the negotiations to end the blockade began in earnest.
Stalin dreamed of unifying Germany under Soviet control but realistically expected the country to be split. His decision to blockade Berlin was part of the strategy to gain as much of Germany as possible under Soviet control before the split. The success of the Berlin Airlift was an embarrassment to the Soviet Union and a major unifying factor for the newly formed NATO. Seeing this Stalin gave up on acquiring a greater part of Germany and wanted to move forward with the plan to establish East Germany.
The cost to the Soviets was PR and Moral. The thousands of planes landing every day were a very visible symbol to the world of the Soviet Unions incompetence and cruelty.
EDIT Stalin's decision seems to have come in February of 1949 nearly 3 months before the end of the blockade and before the Easter Parade. Negotiations had broken down in December of 1948 because there was still the chance that winter would defeat the airlift. By February it had become clear to everybody that the airlift was a success. Stalin still attempted to negotiate as many favorable terms as possible during the next 3 months but the Allies refused to budge and slowly the negotiator for the Soviet Union gave ground on nearly every point. The end of the blockade seemed very sudden because the negotiations were conducted behind closed doors. To keep the pressure on the Allied commanders weren't even informed that there were negotiations until late March.