The term "beyond detection" could mean two things: As objects redshift, they may eventually redshift so much that we don't have the technology do see them. A more interesting interpretation of the term is "is the object detectable in principle?", i.e. with any conceivable instrument that doesn't violate the laws of physics.
Objects that today are farther away than roughly 63 Gly ("billion lightyears") will never be detectable, simply because the expansion of the Universe carries then away too fast for the light to reach us. Objects somewhat nearer than this may also be undetectable, because the light both is redshifted far into the radio regime, and because the rate at which photons arrive becomes so low that they appear too dim for us to see.
But let's assume that the receiving of a single radio wave is enough for us to call it "a detection".
Objects within the 63 Gly have redshifted already, just as all other objects lying at cosmological distance (i.e. far enough that they're not gravitationally bound to the Milky Way).
But the observable Universe always increases in size, because the light from increasingly distant galaxies, as time goes, has had the time to reach us. That means that once a galaxy is within the observable Universe, it never leaves. It may redshift so much that puny humans can't see them, but radio creatures with eyes the size of a galaxy can still see them.
"Comoving coordinates" are defined such that they coincide with the real, physical coordinates today. In 15 Gyr ("billion years") or so the Universe has expanded to twice the size of today (linearly speaking), so the physical distance to the "border" outside which we will never be able to know about will have grown to 126 Gly, and in 25 Gyr it will have grown to 252 Gly. In other words, galaxies always move farther away in physical coordinates, but remain stationary in comoving coordinates (except for small so-called "peculiar" velocities of a few 100 km/s).