In researching the reasons for the prolonging of the Korean war, most sources point toward the defensive tactics of the Chinese which matched the aggression from US/UN forces. But apart from providing indirect (air support, supply contributions) support, how did the Soviet Union contribute to the stalemate?
In "Mao" by Jung Chung, she made a good argument that the real instigator in the prolonging of the war was Mao, while the Soviets apparently weren't excited about continuing support for the war. Mao needed an excuse both to justify support and, (this was the big reason) to demand advanced weapons factories from the Soviets, MIGs in particular. If the war had ended soon after the peace talks began in 1951, it would have been easy for the Soviets to continue with only minimal support for China.
So, along this line of reasoning, the Soviets role consisted mostly of just providing the weapons and supplies,and that somewhat reluctantly. There's an indication of both the reluctance and how central Soviet support was in events of 1953: after years of arguing over things like chair size, or flag size, etc., Stalin dies on March 5, and by July 27 they have the armistice hammered out and signed.
The biggest stumbling block was repatriation of POW's. The North Koreans and Chinese demanded that all POW's be repatriated. However, many of their soldiers had been pressed into service and were either a) not communist or b) South Korean. Sure, there was all the talk about the size of flags and who sat where, but POWs were the crux of the problem.
Any other argument is really a stretch. After the lines stabilized, there was no real "push" to capture more territory. Had there been, the war would've been completely different. At the outset of the war, the South and the US/UN soldiers were caught totally off guard. The Southern lines were overran, the few US soldiers that were there as advisors were captured quickly, the soldiers sent in as part of Task Force Smith were destroyed, and the US/South Korean forces barely held on to the Pusan Perimeter. However, once the US/UN coalition showed up, they were able to push the North Koreans back. It was only the lack of supplies and the overwhelming number of Chinese that pushed them south again. Once the lines were established however, the war could have gone in the US/UN favor. The Chinese/North Korean/Soviet factories were no match for the US factories and their material output. Had the Chinese wanted to, they could have thrown more men against the US/UN forces. At the same time, by mid 1951, the supply issues were resolved and the US/UN forces could have thrown way more against the Chinese had they wanted to. The simple fact was that MacArthur was out, Ridgeway was in, and the directive was to hold the line while negotiations took place.