Why is radiation as natural background radiation still detectable? Isn’t this kind of radiation broken down?

Answer

You can’t “break down” radiation like that. Radiation is photons that move at the speed of light. Only if they hit another object, or pass close to an atom, can they be absorbed. The absorbing object or atom then gains the energy of the photon. Until that happens, the photon will continue to fly around.
The cosmic background radiation is in fact the “heat” of the universe. After the big bang, that radiation was very hot. Because the universe expands, the intensity of the radiation decreases (after all, it has to fill an increasingly larger volume), and due to the redshift the wavelength has become so longer that we now see that radiation as radio waves.

see for example:
http://www.astro.ubc.ca/people/scott/cmb_intro.html