history

The USA under truman originaly didnt care much about the kuomintang since to them losing the mainline mean their didnt matter anymore and he said the US would follow the https://en.m.wikipedia.org/wiki/1943_Cairo_Declaration but then due to the Korean war they adopted the contaiment policy and Truman order the 7th fleet to patrol the strait basically protecting Taiwan from any mainline attack, and that has been the status quo ever since

It's very hard to invade an island

Following the end of World War 2, the US provided substantial aid to the KMT in the civil war, including a naval effort that would prevent the PRC (with its quite limited naval capacities) from a landing in Taiwan.

nuclear weapons from the United States were deployed to Taiwan from 1954 to the 1970s

US invasion of Korea, basically

There was a small window of opportunity where the PLA could have put an end to the KMT since US forces were occupied in Korea, but US forces were approaching the Yalu River. Partly for geopolitical reasons, partly for comradery reasons, Mao chose to intervene on behalf of the Koreans. This, however, meant the KMT was able to consolidate their hold in Taiwan. If you look at the timeline, the PLA was able to liberate a bunch of islands in May 1950, but they entered the Korean War as the PVA in October 1950. With the window of opportunity closed, the PLA could not liberate Taiwan since the 7th Fleet was there to guard Taiwan while the PLA barely had a navy, let alone a navy that was capable of an ambitious amphibious assault.