The universe is largely transparent. Sure, some parts of the radiation have been absorbed, and there is a bit of new emission at this wavelength range, but overall it is not a large effect and it can be taken into account.
>How does the cosmic microwave background persist?
Energy is conserved, and the CMB is mostly not interacting with anything, so it *must* persist. The laws of physics require it.
>Why hasn't it been distorted and destroyed by new sources of energy pumping into space?
Because it doesn't interact directly with almost any of these other energy sources, and there isn't that much energy being "pumped into space" in the first place -- not nearly as much as is already there due to the CMB. There is more total EM radiation intensity from the CMB than all other EM radiation sources combined. The other EM radiation is also at different wavelengths. EM radiation does not self-interact, and it is easy to distinguish radiation with different wavelengths, so the signal of CMB radiation is easily separable from other sources.