In George Orwell's Animal Farm, Mr. Frederick was not mentioned after the Battle of the Windmill. Can we safely assume that his fate was similar to that of Adolf Hitler, his historical parallel?

Frederick shares many traits with the man he is modeled on, Adolf Hitler. He is a liar, a double-crosser, a master propagandist willing to spread sordid and untrue tales of Animal Farm atrocities, and he sneak-attacks Animal Farm in a dastardly way that parallels Hitler's attack on the Soviet Union.
The book, however, is an allegory. In an allegory, characters or things stand for or symbolize something else. While there are correspondences between characters in an allegory and real historical figures, an allegory like Animal Farm is not meant to be an exact, literal retelling of history. It's simply supposed to strongly suggest that there is a parallel. For example, while Napoleon is based on Stalin, Stalin always lived in a house, unlike Napoleon. Napoleon is like Stalin not in all the minutia of his lived experience but in broad outline: both betrayed the ideals of the revolution they were part of out of a lust for personal power, and both used terror to maintain their power.
Likewise, Frederick, in broad outline, acts in a Hitler-like way. He is a sneak, a cheat, and a creep. But that doesn't mean he follows exactly in Hitler's footsteps. For instance, there is no sign that he perpetrates genocide. Nor is his farm overrun by Animal Farm's army and allied armies while he hides in a bunker. Therefore, there is no reason to expect that Frederick commits suicide, nor is it important to the story.

Frederick is the shrewd owner of the neighboring Pinchfield farm, who is known for being "perpetually involved in lawsuits." He attempts to take advantage of Jones's misfortune. Frederick tricks the animals by purchasing timber from them and paying for it with counterfeit bank notes. Shortly after stealing the timber from the animals, Frederick and his troops attack Animal Farm and destroy the windmill before being driven out of the farm by the animals. In the novella, Frederick's character symbolically represents Adolf Hitler, the leader of Nazi Germany during the 1930s and 1940s. Similar to how Hitler decided to attack the Soviet Union during World War II, Frederick chooses to attack Animal Farm, which allegorically represents the Soviet Union throughout the novella. In the novella, Frederick's character is not mentioned after the Battle of the Windmill. Given that the story is the allegorical tale of the Russian Revolution and the early years of the Soviet Union, the plot and action of the story are focused on Animal Farm and Napoleon's reign, not on Frederick's fate. While Orwell chose not to elaborate on Frederick's fate, one cannot assume that Frederick committed suicide like Adolf Hitler. Essentially, there is no way of telling for sure whether Frederick committed suicide like his historical parallel.