Dictionary.com defines "reich" as:
"The territory or government of a German state, as the Holy Roman Empire, or First Reich, from the ninth century to 1806; the German Empire, or Second Reich, from 1871 to 1919; the Weimar Republic, from 1919 to 1933; or the Third Reich, from 1933 to 1945."
Unless I am completely wrong in my interpretation of history, the only one of those associated with Nazism was the Third Reich, which lasted only 12 years.
I know that the Neo-Nazi movement keeps agitating for the establishment of a "Fourth Reich", but I don't see that happening.
In my opinion, my original reply remains valid. If history records the existance of a Fourth Reich, it is likely to be referring to something that will have been established after our lifetimes. It will take time for the memories to fade, but eventually Germany under Nazism will be relegated to the same dusty history books as Russia under Ivan the Terrible or the Roman Empire under Caligula...it just won't matter anymore.