The real answer is that it doesn't stop. We're just used to it.
The fact that hot metal glows red is a quantum effect. In fact, it was the first recognised quantum effect.
Mirrored sunglasses are an example of photon tunnelling.
We can see a quantum superposition using only a beam splitter.
The laser hits the beam splitter from the left and is both reflected and transmitted. The two outputs represent a superposition at the quantum level due to the precise phase relationship.
An apple has a colour that can only be explained using quantum theory. This is otherwise called spectroscopy, but the entire field of atomic and molecular spectroscopy is based on the quantum nature of these materials.
The MRI imaging is based on the precession of the magnetic moments of hydrogen and other atoms. These magnetic moments are explained using quantum theory.
Electron microscopy is based on the wave-like properties of electrons, which are related to the energy of the electron beam.
In essence, quantum theory forms the basis of understanding much of the physical world.
So the real question is, what is classical?
In quantum theory, the classical limit is where Planck's constant can be approximated as zero. This sets a type of scale. In particular, Planck's constant essentially captures how wave-like particles are, and vice versa. It represents a sort of coupling between wave and particle properties.
Therefore take the two most important formulas in the development of quantum theory; Planck's formula, [math]E=hf[/math], and the de Broglie formula, [math]p=h/\lambda[/math]. The first formula gives the energy of a photon, which can be considered a particle of light. By setting [math]h=0[/math], we return to light being purely a wave phenomenon. This can be satisfied in the limit of large energy, [math]E[/math]. With the de Broglie formula, setting [math]h=0[/math] removes the wave-like properties. This is the large momentum limit, where the wave-length is vanishingly small.
Therefore, we expect classical objects to be objects with large energy and momentum relative to Planck's constant. That's where particles behave like particles and waves behave like waves.
For example, the following picture shows classical diffraction.
The quantum case would indicate only a few detected points. The quantum case becomes the classical case in the limit of a large number of point detections. The quantum-ness remains in the statistical noise in the pattern. This is called quantum noise. For a very bright pattern, the quantum noise is negligible.
The elephant in the room is Schrödinger's cat. This was intended as a reductio ad absurdum to demonstrate that quantum theory was incomplete. In this case, it can be represented by a macroscopic superposition of two particle positions. In the context of large quantum number, we don't expect macroscopic massive objects to exhibit wave properties. Superposition is a wave property, as exemplified by the beam splitter picture. So something must give in the classical limit. However, rigorously treating this situation requires a more advanced understanding of quantum theory, in particular, how coupling with the environment affects quantum properties. In essence, we generally lose quantum properties of coherence due to unwanted coupling with the environment. This destroys any superposition, even in tiny quantum systems.
Overall, the quantum nature of reality is all around us, often hiding in plain sight. Much of our deeper understanding of the world around us is based on quantum theory. It hasn't really disappeared. We just are in the habit of not asking, “why is it so?”