I’m not a historian, but i do have insight into modern Japanese economic history.
First, in answering the question why the LDP survives in general (unrelated to Plaza or the Bubble), Umeda (2020) explains rather comprehensively. Here is a general summary.
- The countryside disproportionately favors the LDP due to the farm lobby and the subsidies and protections provided to farmers.
- The business lobby (Keidanren) supports the LDP, which is powerful in swaying public opinion and providing resources to the LDP.
- The opposition has always been weak. There is a general distrust of opposition parties and they are still weakly organized.
- The parliamentary democracy of Japan allows forming coalition governments if the one party fails to reach a majority. The LDP has mostly been able to get the most seats and so forming a government was not difficult.
- The LDP has been adaptable and innovative often stealing ideas from other parties.
- The LDP appears to have stronger foreign policy. With the rise of China and Japans global economic standing waning, the LDP seems to be the strongman populist party.