For how long the Cosmic Microwave Background was emitted?

[SpaceBear]

When the Universe was 379,000 years old, the radiation could travel into space.
From that point in time the CMB started to be emitted in form of visible light.
Am I correct?

my question is: for how long the CMB was emitted? Or is it still emitted today?
If the CMB was emitted for 10 million years, then it should only be available for us to receive for 10 million years, and not longer.
For example if a red giant star is born today 1 billion light years away from us and it lives 1 million years, then we will start to see it after 1 billion years but only for 1 million years. After that million years, it won't be on our sky anymore.

Where am I wrong?

 

[Bandersnatch]

What is now seen as CMB radiation was emitted more or less in a single moment in time.
The difference between it, and a star, is that the star is confined to a limited volume in space, while the origin of the CMB was in ALL of space.

For convenience, imagine 1-dimensional space(that is, a line), on which lie an infinite number(or at least too large a number to care when compared with the age of our 1-dimensional universe) of points that simultainously emit radiation at some moment in time.
Whichever point on the line you chose, there will always be a bit of radiation just passing it by from both sides at once. The later in time it is, the farther on the line with respect to the observer are the points of origin of the currently observed radiation.
If the line is not infinite, but finite and closed(i.e. a loop), you get the same result.
For the CMB to stop being observed, the line would have to be finite and with boundaries, and enough time would have to pass for all the CMB to pass the observer by.

Note that our universe is thought to have no boundaries, but whether it is infinite or not is still anybody's guess.