First, Japan during the Cold War wasn't exactly a major military power as it had a pacifist constitution (written by the good ol USA!) and in any case it was so devastated by WWII that initially they couldn't have a strong military even if they wanted it. This ensured that it was no longer a threat to the United States. Japan's main role during the Cold War was to provide a giant base for the US military (a role it still inhabits today).

Second, we won the war. It's easy to be forgiving when you've already gotten payback and dropping two atomic bombs then occupying their country for years seemed like more than enough to call it even.

Third, the enemy of my enemy is my friend. Even before the war ended there were people (including MacArthur) who predicted that Japan would be an important ally against China and the Soviet Union. During the Cold War people were so worried about communism that holding old grudges weren't that important. China had been an ally but that was Nationalist China, communist China was viewed as a serious adversary until Nixon.

Fourth, the Cold War lasted a really long time and new generations arose who were very young (or hadn't even been born) when the Second World War happened

Finally, there were some people who viewed Japan as a potential threat, particularly in the 80s when Japan's economy looked like exceed the United States'. Many viewed Japan's economic miracle the same way people today view the rise of China and some predicted that Japan's economic growth would inevitably lead to a military confrontation. George Friedman's book The Coming War with Japan is a good example of this line of thinking.

The US defeated Japan, occupied Japan, wrote their constitution and kept it as a satellite state. Article 9 in the Japanese constitution written following the fall of the Meiji dynasty enforced Japan as a pacifist state, renouncing all military actions unless in self defence.