Has cosmic microwave background kept a constant frequency? Has the frequency of CMBR changed at all since the beginning of the universe? Has it always had a microwave frequency or has the frequency increased/decreased over time or is the change due to factors such as the Red/Blue shift? 
 A: No. Light travels at the speed of ... light, when measured locally in inertial reference frames. And the relationship between wavelength and frequency is $\lambda = c/f$.
As the universe expands, the wavelength of the cosmic microwave background photons is "stretched" and thus their frequency must decrease by the same factor of $(1 + z)$, where $z$ is the redshift.
Thus the wavelength has gradually increased and the frequency decreased - from being red/infrared photons at $z \simeq 1100$ when the photons decoupled, to microwaves now.
A: Theoretically, the CMBR is what we see of the early visible universe. If we could be there to observe it, we might see much higher frequency radiation. However, due to the expansion of the universe, the wavelengths got stretched out and the frequency redshifted. Or perhaps you can say in our reference frame, we happen to measure these photons to be microwaves.
A: Has the frequency of CMBR changed at all since the beginning of the universe?
The usual answer is yes. It's thought to have redshifted by a factor of a thousand. 
But there is an issue: conservation of energy. Where did the energy go? This is an intriguing thread to pull, because we don't know of anything that's in breach of conservation of energy. There are no perpetual motion machines. Gravitational field energy is positive. And when it comes to gravitational redshift, the usual answer is wrong. A descending photon doesn't gain any energy. You know this because you know that when you send a 511keV into a black hole, the black hole mass increases by 511keV/c². In similar vein an ascending photon doesn't lose any energy. There is no magical mysterious action-at-a-distance mechanism by which a photon in space gains or loses energy. What happens is that when I lift you up I do work on you. I exert a force for a distance, and you gain energy. So the photon looks like its lost it. Then when I drop you some of your potential energy is converted into kinetic energy which gets dissipated, so you lose energy and suffer a mass deficit. So the photon looks like it's gained energy. You see the photon as blueshifted because you and your clocks go slower when you're lower. Because the "coordinate" speed of light is lower. Or you see the photon as redshifted because you and your clocks go faster when you're higher, because the "coordinate" speed of light is higher. You can see Einstein talking about the speed of light being spatially variable in the second paragraph here. Also see Baez. 
As for the CMB, IMHO it's possible that the same sort of thing could be going on. The  universe has a spatial energy density, and conservation of energy says its reducing. This is not totally unlike climbing out of a gravity well, where the spatial energy density reduces with distance. For the expanding universe it's reducing over time. As a result the coordinate speed of light is increasing, and the CMB photons appear to have lost energy. But actually, they haven't. It's just that in the early universe, everything was subject to something like gravitational time dilation, and was going slow. If you'd been around then with a clock, your clock would be going slow, but you wouldn't know it. Now you and your clock are going faster, so the CMB photon frequency looks like it's reduced, when actually it hasn't.        
