Is the total energy of the CMBR diminishing with time?
Yes. The energy density in the radiation field scales like $a^{-4}$, and the volume scales like $a^{3}$. Since the total energy is the density times the volume, the total energy scales like $a^{-1}$. Note that $a$ is called the "scale factor" and $a = \frac{1}{1+z}$, where $z$ is the redshift, assuming $z=0$ now.