This is a good question. So many encyclopedia entries, passing mentions in books, etc. pass up the issue of ending the blockade, as if the motivation for dropping it was obvious. Daniel Harrington, in a mid-1980s round up and revisit of the arguments over the crisis, gives a typical example of this, "By mid-March, with the worst of the winter behind him, Stalin realized that whatever leverage the blockade afforded was shrinking rapidly" [3:110] This is true even in very recent accounts. Ted Hopf's book on the early cold war, writes, "After the airlift demonstrated its capacity through the winter, Stalin dropped his currency demands..." [2:141] which were the final obstacle to coming to resolution.
Usually there isn't much attempt to explain why he couldn't continue the blockade another year, two years, etc. The assumption I think many people make, even when works don't really show any evidence that Soviets thought this way, is that the political cost in terms of loss of international reputation was high, and not worth dragging the crisis out. My quick look through the literature didn't say much in detail on this however, but perhaps someone can chime in. Part of the problem, I think, is that the overwhelming predominance of literature on this subject seems to use almost exclusively Western sources (would be great if someone could point out recent work which makes use of Soviet archival sources).
I found one important exception to the above in the form of a 1997 article by William Stivers 1 in Diplomatic History which is frequently cited in subsequent works and encyclopedia entries on the subject of the Berlin blockade. I'm frankly surprised to see no integration of its findings into the Wikipedia entry on the blockade.
I saw three major takeaways from the Stivers piece that can help us answer your question:
The literature fundamentally distorts the facts on the ground during the conflict by portraying (as Allies did at the time) the situation in Berlin as creating a fully isolated city. As Stivers puts it and argues in detail in the article, “the Soviet blockade neither attempted nor achieved the isolation of West Berlin” [1:569]
No effort was made, however – either at the beginning of the blockade or during the course of it – to seal off the Western sectors from either East Berlin or from the surrounding countryside. As a result, a flood of goods – roughly a half a million tons, to take the mean of various estimates – entered the Western sectors from Soviet area sources over the ten-and-a-half-month period of “restrictions.” [1:570]
Many works, including the wikipedia entry note that there was food offered from the east but, "they do so chiefly to emphasize that the great majority of Western sector residents turned it down.” [1:571]
Speaking to your suggestion that the Soviets could have just continued indefinitely, Stivers suggests even more strongly:
East German and Soviet aims – once asserted with breezy certainty by Western historians – become suddenly elusive. In particular, the fact that the Soviets imposed the blockade, but then let it be undermined in a way that assisted the West to victory, is a contradiction in search of explanation. The Soviets probably could have “won” the conflict at any number of points. Had they imposed an absolute blockade at the very beginning of the crisis (thereby reducing the Allies’ cushion of time), or slogged on with it indefinitely ... they would have strained morale to the limit. [1:595]
He answers this puzzle by emphasizing the fact that it was not the isolation of Berlin that they wanted, but the further integration of it into an economy that had great benefit for interaction with it [1:595] While all eyes are on the symbolism of the air-lift for relieving West Berlin, less attention is paid to the powerful impact of the counter-blockade on East Germany:
The East German economy suffered grievously from the Allied counterblockade imposed...against Western zone shipments to the East. Trade with Berlin’s Western sector companies helped reduce the damage of shattered interdependencies and avert collapse in certain key sectors. [1:587]
In this perspective, Stivers there was both an economic and a political cost - but here the political cost is not just internationally but in terms of its intra-bloc reputation as well:
As it was, the blockade was a massive blunder. In German eyes, not only did the Soviet Union appear a most implausible “friend,” but the necessity of seeking security with the West seemed conclusively proved. Economic considerations aside, Soviet supply and trade offers – beginning with the milk offer five days after the blockade began – look like efforts to deescalate the crisis in order to repair political damage. [5:596]
Finally, Stivers makes a complex argument, not considered in detail here, that the conclusion of the crisis, which hinged on the Soviet dropping of its demands, especially regarding the currency in West Berlin, came partly as a result of British resistance to certain aspects of American demands, and stalling actions by the British and French up to a point where the demand simply made little sense anymore, thus easing the way for a resolution to the crisis. The period of the blockade brought about changes in the economic environment and decreased the interdependency of the two sides to a point where the restoration of the pre-crisis state was increasingly unlikely. [1:602]
In conclusion, Stivers argue, reproduced by others who cite him in later works, is that the blockade came with a cost to the Soviets that was both political and economic in the form of the counter-blockade by the Allies on East Germany, and during its course, helped bring out economic changes in the relationship between East Germany and West Germany that made restoration of the pre-crisis status quo difficult and thus not worth the continuation of the blockade.
Sources refered with above as [Source Number:Page Number]
William Stivers, “The Incomplete Blockade: Soviet Zone Supply of West Berlin, 1948–49,” Diplomatic History 21, no. 4 (October 1, 1997): 569–602. Wiley Online
Ted Hopf, Reconstructing the Cold War: The Early Years, 1945-1958 (Oxford University Press, 2012). Gbooks
Daniel F. Harrington, “The Berlin Blockade Revisited,” The International History Review 6, no. 1 (February 1, 1984): 88–112. Jstor