Chiang Kai-Shek was kidnapped in 1936 in what's known as the "Xi'an Incident". Essentially, in the face of a fierce Japanese offensive, Nationalist leaders were frustrated with Chiang's seeming obsession with eliminating the Communists. They felt that it was undermining the Nationalist effort to resist the Japanese, so several generals, including Zhang Xueliang, redirected Chiang's train, and forced him to sit down with the Communists to sign a truce and agree to unite against Japan.

In regards to why the Nationalists fell so easily to the Communists, there are a couple of factors:

1. Poor morale by the common Nationalist soldiers. Most of these soldiers were conscripts, and were both ill equipped and unmotivated to fight the Communists. They were fed starvation rations, and were sometimes chained in groups and forced to advance or be shot in the back. The result was mass defections from the Nationalists to the Communists. In 1946, there were roughly 4.3 million soldiers for the Nationalists and 1.2 million for the Communists. By 1949, the Nationalists had about 1.5 million soldiers and the Communists had over 4 million.

2. High morale among Communist soldiers and support. During the time of the Civil War, over 90% of China's population was rural, and the Communists had spent the last twenty years creating a positive image of themselves - in fact, Mao's focus on the peasantry driving the Communist Revolution in China was a major source of tension with the Soviet Union. Joseph Stilwell, an American general who served in China and Burma during WW2, noted that the Communists enjoyed enormous support and high morale; both the soldiers and the common people believed in their mission and leaders. Stilwell had a horrible relationship with Chiang, which undoubtedly resulted in his scathing critique of the Nationalists, but his account nonetheless indicates the popular support propelling the Communists.

3. Poor morale among the Nationalist leadership. Rampant corruption withered morale and the finances of the Nationalists, and by 1946 they were drowning in debts. Following a rapid series of CPC successes in Northern China in 1948-early 1949, Chiang quickly resigned and Li Zongren took power. However, the fractious GMD politics continued; against Li's wishes, Chiang moved the majority of the nation's gold and USD reserves to Taiwan in April 1949, which resulted in Li resigning.

These are some of the major reasons for the Communist victory. There are some others, but in my opinion, they are ancillary to the ones listed above. For example, the acquisition of Japanese weaponry in Manchuria is significant, but would have had a minimal impact on the war if the Nationalists were not hemoragghing soldiers.

Were there any key moments that could have changed the course of history? Well, if the Shanghai Massacre didn't drive Mao to the countryside, the Chinese Communists may have remained a relatively small political party confined to the urban areas. If Chiang had been allowed to continue his attacks on the Communists, he might have wiped them out, but his government seemed doomed to fall by that point. Essentially, China's situation was so critical during the early twentieth century that the Nationalist loss was almost inevitable. Rebalancing the scales in their favor would require altering the nature of Nationalist leadership and world events to a degree beyond a single event.

Sources:

The Rise of Modern China, Immanuel C. Y. Hsu. (1970)

The Search for Modern China, Jonathan Spence (1990)

China: A New History, John Fairbank (2006)

I talk a bit about this here and here.