The so-called Third Reiche was unstable. Hitler was - rightfully - suspicious of those in his ranks. He would often freak out and act the fool, to keep them offguard, so they wouldn't know what to do with him, or how to read him. The Nazi Party was the product of its time, as I've said. Not only because it revolved around Hitler, but because books, newspapers and word of mouth were the only way information was kept and passed around. And the Nazi's made damn sure to burn or ban books containing ideas they were frightened by, or suspicious of, or just didn't like. The other side of that was the false propaganda, the official spin on their own wrongs and failings, and the outright lies that were necessary to keep a situation contained. And one of several reasons for their starting wars was, quite simply, to keep themselves in profit and power. The worst about this "Undefeated Nazi Timeline" is that it reveals just how ignorant its creators are about World War II.
Then I suggest one would have to amend this timeline to reflect the Nazis being involved in a long cold war with the US and/or the USSR. In light of the origins of WWII, as you and others have succinctly put it, the Nazis would have to keep the German people in a state of constant paranoia and hyper-angst in order to remain in power at all. The USSR at their eastern border as a constant existential threat (which indeed it would be) would be important for that condition, as would the USA's never-ending antipathy.
The other side of the coin is that an undefeated Nazi party possibly means an undefeated imperial Japan. This new speculative world is likely to be a VERY violent place with several enormous military industrial complexes competing for dominance in hot and cold wars. Wherner Von Braun would have plenty of opportunities to piggyback his exploratory agenda on the colossal funding of a Nazi ICBM program (just as he did in the USA after the war, just as Korolev did in the Soviet Union).