There are a few main reasons.

The first would be Mao's land reform, which was immensely popular, which helped to gain him the peasantry's support, which is something the Kuomintang wouldn't of been able to do, Mao had previously cooperated with local peasant associations (early 1940s) to reduce rent and taxation (so that he didn't completely alienate the landlords, he'd do that later). The CCP were also able to provide famine relief, revive the silk industry and production cooperatives. He also gained support through 'speak bitterness' trials, which later evolved into 'struggle sessions' (after the war), where the peasants would be encouraged to publicly humiliate landlords for class crimes (like owning land).

Another is the failure of nationalists to properly rally support, from their own country and other powers. After the nationalists had reconquered land that the CCP had taken they'd often just reinstall the previously humiliated landlords, which would obviously upset the peasantry. The reconquering of land can be summarised as the nationalists bring corruption, neglect and chaos. Furthermore Chaing Kai Shek continued to cooperate with administrators who had worked with the Japanese, which would've obviously weakened his aim to be a nationalist icon. Additionally the GMT originally had a huge amount of support from the USA but as the USA's foreign focus were constantly elsewhere (Europe) and the corruption that plagued the Kuomintang made the USA only willing to continue to support them, in spirit, because of their fear of soviet influence in China.

Another failure of the nationalists would be hyperinflation, the nationalists printed money to fund the war effort, which inevitably created hyperinflation. This resulted in waves of strikes (e.g. in Shangai in 1947) and a steady rise in unemployment. The government tried to implement wage and price fixing, but these both failed, eventually they attempted to stabilise the currency with gold but this was short lived as they over-printed the new currency which led to hyperinflation again. Essentially the nationalists got their strength from urban areas, and as they failed to reduce the widespread corruption, and other issues, they alienated a large percentage of the population who had previously supported them.

The final factor that I'll be talking about would be the actual army. The communist army possessed a much higher morale fueled by a revolutionary zeal, by comparison the nationalists used forced conscription, and had incredibly high desertion rates, with conditions brutal and rations poor. The CCP would retreat whenever they encountered superior numbers and only attack to wear the enemy down.

This is only the second time I am contributing here so if this answer doesn't fit, I feel free to remove or correct it.

This is a complex issue, but I would say it is primarily down to Mao being the right man at the right time, and Chiang Kai Shek being incompetent in dealing with his own weaknesses, and ineffective in using his strengths.

Mao Zedong, through a mixture of personal talent and political instinct was able to withstand and eventually overcome the many obstacles put in his way by the Nationalist government of China. On the other hand, Chiang Kai Shek, who you might know was the leader of the Guomindang or nationalists, was unable to make use of his own advantages as a result of a combination of personal failure and external pressures. To understand the roots of the ultimate communist victory, we have to look at the course of the Chinese civil war(s) from 1927 to 49. In the Jiangxi period from 1927 to 1934, Mao established himself as a key figure and leader in the CCP and through ideological and military reforms allowed it to survive, while Chiang Kai Shek’s inability to do so caused his failure in completely destroying the CCP. After being driven from Jiangxi, concluding the long march with the arrival of the CCP army led by Mao in Yan’an in 1935, the second period began. This saw Mao refining his ideology and consolidating his power while the second sino Japanese war raged throughout the country, degrading the GMD’s power and legitimacy. Once World War Two ended in 1945, the second Chinese civil war erupted, in which the CCP used the few advantages they had to their fullest, in order to survive. This then allowed them to defeat the GMD, who were weakened by economic and social issues, as well as the ineptitude of their leader Chiang Kai shek. Mao Zedong’s policies and strategy consistently and correctly assessed and addressed the situation in the country, while Chiang’s own strategy failed to solve fundamental problems, that would ultimately lead to his downfall. 

Mao’s brand of guerilla warfare and development of rural communism allowed him to excel under the circumstances of the Jiangxi period between 1927 and 1934, while Chiang’s grand strategy was the primary factor hindering him. It can be claimed, with certainty, that Guerilla warfare and a policy of seeking peasant support facilitated the CCP’s survival in rural Jiangxi, even through successive military attacks. These ideas of rural communism and guerilla warfare were those of Mao. Mao, who initially diverged from the party line in pursuing a ruralist strategy and distrusting the GMD, was vindicated in his views by Chiang’s betrayal of the CCP in the Shanghai massacre and the following white terror. The attempts of the party leadership in fighting a conventional war over the control of the cities failed, while Mao’s talent for strategy became evident through the success of his ideas in building and maintaining the Jiangxi soviet. Through his strategies he enabled the survival of the CCP, who, driven from their traditional urban bases, had nowhere to go except the safe haven he built in Jiangxi, in the south of China. Mao was then also able to, through guerilla warfare, defend this base from a superior force in four attempted encirclement campaigns by the nationalists. However, to give Mao all the credit here would be to ignore the also crucial role in the survival of the CCP played by Chiang Kai Shek who failed to destroy the communists, perhaps even more importantly, due to his own faults. 

Chiang’s lack of effective strategy and political control over the country allowed the CCP to survive and escape. This can be seen when GMD were troops repeatedly beaten back by guerilla warfare, with four encirclement campaigns ending in failure. Yet, Chiang didn’t improve his strategy on his own. His lack of political control came back to bite him when a warlord, supposedly fighting on his side, allowed the CCP to escape on the long march in 1934. This made an almost certain victory in the fifth encirclement campaign a failure in its goal of finally destroying the CCP. Even this eventual half-victory was not due to Chiang, but to the German general von Seeckt and foreign support, advising him to use a slower blockhouse strategy to strangle the CCP. Because of this, it can be said that the GMD had the potential for military success, but their leadership was incompetent. While his army were successful in driving the communists from their base, Chiang himself had failed. This failure becomes even more apparent in regards to his political strategy. Chiang had contributed to uniting large parts of China via bribery rather than the conquest of the many warlords that ruled over much of the country. As a result of this, he hadn’t consolidated his rule over China, with large sections of his army consisting of warlord troops who didn’t fight as effectively as the GMD’s own troops who, in their lack of loyalty to the central government, let the communists escape. This performance was very much the opposite of Mao’s leadership style, which, from the start, consisted of centralising and consolidating his power in the party.

Since Reddit limits comment lengths I will have to split it into multiple comments