In our theoretical alternate universe Nazi Germany--thanks to its scientists that in real history were split and used by the US and USSR--managed to reach the level of nuclear warheads and ICBM technology that the US accomplished in the early/mid 1950s, producing systems comparable to the Atlas and Titan ICBM projects (range of 5,000 - 10,000 miles).
Scraping up funding, they produce 12 such ICBMs, complete with nuclear warheads, and had them online as of late November 1944, about six months before the actual invasion of Berlin by the Allied Forces in real history. Two of the ICBMs were used, one as an example on the Eastern front, and one as an example on the Western front (the exact targets are unspecified, answers may select locations if they feel targets are material to the question). After these examples, the Allies decided to sign a ceasefire and hostilities on both sides were stopped. Part of the ceasefire allowed Nazi Germany to continue to occupy all of the land it currently possessed.
The Pacific Theater continued along a path roughly characteristic to our own history, ending with America dropping the two nuclear bombs on Japan; Nazi Germany does not act to interfere with this theater per the terms of the ceasefire. The Empire of Japan signs unconditional surrender.
The question becomes: Given both the internal factors within Nazi Germany and the external pressures from the growing Cold War (in whatever the cold war might take in this alternate universe) is Nazi Germany stable enough to probabilistically survive to modern day?
If it would not survive to modern day (due to either internal politics/structure or external forces) what would enable it to do so?