As I understand it, some billions of years ago, the universe used to be opaque (edge of the sun - orange colored). Due to the expansion of the universe, photons emitted billions of years ago from billions of light years away are just now reaching us with their wavelengths now shifted into the microwave spectrum. This is what we perceive as the CMB. It seems that the origin of CMB photons just barely lies inside our observable universe. Is this coincidence? Or is there some reason why it should be inside our observable universe? Will it eventually recede outside our observable universe, so that future physicists will look out into space and see no CMB?
The CMB originated everywhere at once, and every spot in the universe has been receiving CMB photons ever since it first started. To simplify matters, forget for a minute about the expansion of the universe, since its only effect is to redshift the radiation. Pretend the "release" of the CMB is happening right now. If after a minute you look to the sky, you will see radiation coming from everywhere. The photons that are hitting your eye originated one minute ago, and so they all were born on a sphere centered on you with a radius of one light-minute.
Now wait a year and point your telescope at the sky again. You still see radiation everywhere; the birth of the CMB was a while ago, so the photons that you see now are those that come from farther away: they formed a sphere with a one light-year radius.
It goes on like that. Again, the CMB was formed everywhere and radiation came out in all directions, and whenever we look at the sky (with the appropiate equipment) we see it coming from everywhere. The reason we see it now is not that the expansion of the universe somehow delayed it; it's just that some of the photons originated very far away, so they are only now getting to us.
As I said, the expansion of the universe redshifts the radiation. This means that as the years go on (and we're talking many millions of years in the future) the wavelengths get longer and the energies smaller, so eventually different instruments will have to be used. In the far future if someone still looks at the sky they might just see a static field instead of radiation.
If our universe is finite, then it is possible that at some time in the future, the CMB will no longer be within the observable universe. This is because the distance that light has to travel from the CMB source to the observer will be greater than the distance between any two points within the finite hyper-spherical universe.