I'm not an expert on it, and all my sources are at home, but essentially, for a very long period of time, the main opposition party was the Social Democratic Party/Japanese Socialist Party, but they were not fully unified as a voting bloc. Some factions were more conservative, others more on the Marxist end of the spectrum. They were organized on a more idealogical spectrum, while the LDP rarely held any unified ideology.

The LDP was often NOT the majority party, nor even always the plurality. But the LDP was almost always able to create a governing coalition when they did not have a majority, and even when the JSP had a plurality, they could not leverage that into a ruling coalition.

The LDP also got lucky in that they were able to take credit in many ways for the "Economic miracle". The LDP could point to the explosion of economic growth in the 60s as evidence of their policies, and were able to use that to remind voters year after year. They were also successful at controlling a great deal of the bureaucracy, including Postmasters (which remained a very influential position in local Japanese politics). Fears of the Soviets also served as a way to attack the JSP, in which some factions did favor turning towards the Soviets. And after their initial successes in the 50s and 60s, they became fairly entrenched. Their popularity in rural areas (which had a disproportionate number of seats, as well as higher voter turnout) led to a system of patronage, which ensured that support would continue from these groups. This corruption would take its toll over time, but not for decades.

Source: I took a class on Japanese Politics since WWII a few years ago, and I still have all of my books. If I recall, three of them were -The Art of the Gut Robin M Le Blanc, University of California Press, 2009 -Japan Transformed: Political Change and Economic Restructuring, Frances Rosenbluth and Michael Theis, Princeton University Press, -Evolution of Japan's Party System, Leonard Schoppa, University of Toronto Press, 2011