The two most famous paradigmatic examples of de-unification are phlogiston and ether. The Kaluza-Klein theory of gravity and electromagnetism did not get to spread as far and wide before faltering.
The phlogiston/caloric theory was able to unify chemical and thermal phenomena in a way that was eliminated by the mechanical theory of heat. Specifically, the processes of heating/cooling were assimilated to chemical reactions with phlogiston (later caloric), and this was one of the key arguments in 18-19th century for preferring this theory. Stahl explained burning and decalcination (formation of metals) by separation of phlogiston from matter in 1703. Black's work in 1757-1764 led to the explanation of latent heat by phlogiston's ability to combine chemically with matter, and of gaseous states as solutions of liquids in phlogiston. Even Lavoisier, who introduced the oxygenation theory of burning in 1780-s, needed a heat fluid (renamed into caloric) to make his theory work. For more details and references see What are the major flaws of the “caloric” theory of heat?
Ether offered a unification of wave phenomena with hopes of extending it to an intuitively appealing unified theory of matter. Kelvin's theory of vortex atoms and Lorentz's theory of electrons were steps in that direction. Suffice it to quote Michelson from 1902:
"The day seems not far distant when the converging lines from many apparently remote regions of thought will meet... Then the nature of the atoms, and the forces called into play in their chemical union... the explanation of cohesion, elasticity, and gravitation — all these will be marshaled into a single compact and consistent body of scientific knowledge... one of the grandest generalizations of modern science ... that all the phenomena of the physical universe are only different manifestations of the various modes of motion of one all-pervading substance — the ether."
The ether loss was taken particularly hard, it still has its adherents, and even Einstein (1920) mused about reconceptualizing it:"We may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an Aether. According to the general theory of relativity space without Aether is unthinkable...". Dirac (1951) suggested identifying it with the quantum vacuum:"The Aether is no longer ruled out by relativity, and good reasons can now be advanced for postulating an Aether... We have now the velocity at all points of space-time, playing a fundamental part in electrodynamics. It is natural to regard it as the velocity of some real physical thing."
More generally, de-unifications are examples of what is termed Kuhn loss, benefits of a prior theory that do not carry over to its successors, see Examples of Kuhn loss? The topic is controversial. In recent decades the disunity of science thesis has gained popularity, it is argued that there are insurmountable obstacles in unifying physical and biological concepts, for example, or biological and psychological ones. In The Conceptual Foundations of Renormalization Theory (1993) Cao and Schweber describe the effective field theory approach that opposes the "theory of everything" even in physics:
"This position rejects uncompromisingly the idea successively advanced during the last fifteen years by grand unified theorists, supergravity theorists, and superstring theorists that the development of fundamental physics will end with the discovery of an ultimate, definitive, and conclusive mathematical formalism. Rather, the development is taken as a process of successive extrapolations that is assumed not to have an end, with every step of the extrapolation being justified by a collective reinterpretation of theory and observation before and after the extrapolation".
Presumably, the reinterpretations should be expected to involve de-unifications with previously unified phenomena coming apart at higher resolutions.