Does something prevent superposition at our scale? I often encounter the argument that quantum mechanics reduces to classical mechanics at sufficiently big scales, as soon as h becomes sufficiently small respect to the actions involved. I clearly understand this for the uncertainty relations. 
But when it comes to superposition, what is preventing it to happen at any scale? Is there actually something that prevents superposition for system bigger (in spatial or any other dimension) than some threshold? 
As a practical example, is there an insuperable limit in how many q-bits we can have in entanglement? 
 A: Nothing prevents superposition at macroscopic scales. Schrodinger's cat states exist according to the Schrodinger equation. If they didn't, it would violate unitarity.
What we don't get is interference at macroscopic scales. One reason for this is that macroscopic objects simply have very short wavelengths. So, e.g., you can't observe double-slit diffraction with a baseball, because the diffraction angles would be too small. Also, the baseball's phase gets randomized too rapidly by interactions with its environment. This is called decoherence.

As a practical example, is there an insuperable limit in how many q-bits we can have in entanglement?

Not in principle, but in larger and larger systems it gets more and more difficult to prevent decoherence.
A: As you are already aware, classical mechanics (which includes the principle of superposition) breaks down at a quantum level, yet holds at more macroscopic levels, due to the effect of h meaning that quantum effects become greatly reduced as momentum of an object increases.
This trend only keeps going, even as we tend to colossally large objects/systems. In fact, something like a galaxy should follow classical mechanical laws even closer than we humans do, albeit to a negligible degree.
So while there is a limit on the validity of the principle of superposition as we decrease our observation size to nanoscopic levels and beyond, there is absolutely no upper bound we know of.
