Nazi Germany was based on a strong ideology and I can't imagine this way of thinking disappeared just like that after the war. I found some anecdotical evidence while browsing the Wikipedia page on German POW camps in the USA.
Often members of the Afrika Korps who had been captured early in the war during Germany's greatest military successes,[13]:150–151 they led work stoppages, intimidated other prisoners, and held secret kangaroo court for those accused of disloyalty. Those convicted were sometimes attacked or killed in a process known as the "Holy Ghost"; most prisoner "suicides" were likely murders.[7][18][15] While the American government executed 14 Germans after the war for murdering other prisoners in three incidents, hundreds of such murders may have occurred.
Prisoners regardless of ideology often taunted their captors, such as saluting with Sieg Heils when forced to attend the lowering of the United States flag. They secretly celebrated Hitler's birthday and other Nazi holidays after the Americans banned them, and many became upset when Jewish American officers supervised them.
So it's clear the ideology survived but I'd like to learn more about how exactly it survived (did it also exist out of POW camps for example) and how long it remained strong.
First thing you need to remember is that not all Germans during WW2 were actual supporters of the Nazis or their ideology. Certainly some were but as with any dictatorship a lot of people just wanted to get on with their lives and didn't necessarily involve themselves with the ideology more than was socially necessary.
A large part of the Nazi ideology was based around the idea that Nordic people or Aryans were naturally superior to other races. Their defeat in the war pretty well destroyed that notion outright. The fact that they had lost the war along with the large amount of suffering that many Germans experienced in the later years of the conflict lead to a situation where many Germans were far from supportive of the Nazis by the time it was all over, if they ever had been to start with.
Of those left that still believed in the ideology at the end of the war, plenty committed suicide, feeling it was better to die rather than live in a world without the Nazis and many more were forced to flee in order to escape justice.
So, by the end of the war you really have a fairly small group of Germans left who are willing and able to carry on the ideology and that group shrinks even more when Germany is divided between east and west and the cold war gets going as most Germans were simply trying to get on with their lives.
There were certain resistance groups that attempted to wage some form of Nazi resistance but they were scattered and unorganized and were generally either hunted down and destroyed or sort of just faded away. From what I understand these were more common in the Soviet controlled zones. They were nicknamed wolverine battalions but I think this was a name only given to them later on.
To an extent there were Nazi communities in South America where some fled in order to escape arrest but again, these were small and the main Nazis living in these places were hunted down in the following decades.
Finally, the neo Nazi movements of today are really totally removed from that original ideology. They lack a single strong leader and a core direction or strategy. They are more a bunch of outsiders wanting to feel power over someone and whilst that was certainly a part of the appeal of Hitler it really went far deeper than that.