The light will become redder (longer wavelength) and redder (longer wavelength) until almost all the emitted light will be in the infrared. At this point you wouldn’t be able to see them even with a super giant telescope, although we can still see them in telescopes that use imaging systems capable of seeing in the infrared.
The James Webb Space Telescope has been specifically designed to look in the deep infrared precisely because these distant objects are redshifted so much.
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