Popularity of the people who vote. He had parliament pretty much in his favor until he started acting overly arrogant and then he lost majorities of the parties who supported him.And near the end of Bismarck's service, it sure seemed like the common man knew what was best for Germany more than the monarchy did.
You are talking about the guy who ran the government extralegally for 5 years because the Reichstag wouldn't give the king the budget he asked for right? One of the biggest things Bismarck did was ignore parliament and do everything in the name of the King and later Emperor. Bismarck lost the presidency because he was not sufficiently willing to be as risky in diplomacy as Wilhelm II was. Do not forget that one of the treaty's that was key in igniting WWI was the Franco-Russian Entente, which, if Germany had renewed the re-insurance treaty with Russia would never have been signed. Bismarck kept Germany out of war and actively worked to ensure that potential threats were neutralized diplomatically while still allowing Germany to grow her economy. It was the dismantling of Bismarcks diplomacy that that led to the tangled web of alliances which, in concert with the recklessness of Wilhelm II, led to WWI
Didn't he eventually get the military budget he asked for though?
Yes but only by cowing the Parliament rather than listening to them. The Reichstag approved his budget in order to stay relevant because he had sidelined them and in many ways turned it into nothing more than a debating society. The Reichstag was neither liked nor wanted by the King, it was an outgrowth of the 1848 revolutions.
How about the First Triumvirate of Rome (Crassus, Pompei, and Caesar)? Or the Second Triumvirate formed by (Octavian, Marc Antony, and Lepidus)? I'm not sure this is a diplomatic example like you are asking, but it's diplomacy of some sort anyway.Or how Muhammad allied with the Jews to take Medina and Mecca away from the Quraysh tribe?