It's because the centre of pressure is an abstraction which does not describe what's really happening on the wing.
The reason it "goes to infinity" is that it's an attempt to define all the forces acting upon the wing as a SINGLE point force, the position of which tells you something about the pitching moment being applied.
Now, if a wing is generating 1kN of lift at the leading edge, 1kN at 25% chord, 0.5KN at mid chord and 0.25kN at 75% chord and at the trailing edge, thats a total of 3kN of lift.
Taking moments about the leading edge, it's 1.0*0% + 1.0*25% + 0.5*50% +0.25*75% + 0.25*100% = 0.9375kN-chords of moment.
So, in this case the CP would be at 0.9375/3.0=31.25% chord.
That's all straightforward.
Now, my wing truly stalls and generates ZERO lift, but being cambered it is still generating some forces, just they sum to zero.
0kN at 0%, 50% and 100%, 250N UP at 25% and 250N down at 75%; total LIFT = ZERO.
There is, however, a moment about the leading edge still - it's 0.25kN*25%-0.25kN*75%=-0.125kN-chords.
To get the CP, simply divide the moment by the lift and, er, oops. Divide by zero error. Infinity.
Simply, the attempt to reproduce the combined moments and forces acting on an airfoil by a single point force breaks down as the nature of the forces more closely approaches a pure couple - so as the lift gets smaller, the 'meaning' of CP becomes less and less physically plausible.