galaxy - How long until we cannot see any stars from other galaxies?

First of all, we can't see stars from other galaxies (with a few exceptions, Cepheid variable stars for example are regularly used to determine distances to nearby galaxies). As it currently stands, we can only see stars from our own Milky Way (in which I'm including the large and small Magellanic Clouds). Type Ia supernovae aside, it might be possible to see Cepheid variables in the Andromeda galaxy, but anything further is almost certainly not possible.

The relevant number when it comes to the distance one could possibly see in the universe is the comoving distance to the cosmological horizon. This horizon defines the boundary between what can be seen and what cannot be seen, simply because the universe is not old enough for particles to have traveled that far (yes, even at the speed of light; in fact, if we're talking about what we can observe, the photon is the particle we care about).

The definition of the comoving distance is:

$$chi = frac{c}{H_{0}} int_{z=0}^{z=z_{Hor}} frac{dz^{'}}{E(z^{'})}$$

where the function $$ E(z^{'}) $$ contains your choice of cosmology (the following is for flat universes only):

$$E(z^{'}) = sqrt{ Omega_{gamma} (1+z)^{4} + Omega_{m} (1+z)^{3} + Omega_{Lambda} }$$

This distance can be extrapolated out into the future (given your choice of cosmology), and ultimately will tell you what the distance to the cosmological event horizon will asymptotically reach. This is the distance at which no object beyond could ever come into causal contact with you.

Another simpler way to calculate the particle horizon is to calculate the conformal time that has passed from the beginning of the universe, and multiply it by the speed of light $c$, where the conformal time is defined in the following way:

$$eta = int_{0}^{t} frac{dt^{'}}{a(t^{'})}$$

where $a(t^{'})$ is the scale factor of the universe, and its relationship to time depends specifically on your choice of cosmology. Again, if the ultimate value of this horizon is desired, you would need to integrate this to infinity.

SUMMARY: I'm having a hard time finding the exact number of the comoving size of the cosmological event horizon, though I'll keep searching. If I can't find it I suppose I'll have to do the calculation when I have some free time. Almost certainly it is larger than the size of the local group of galaxies, making our night sky largely safe from the fate of the universe. Anything further than this horizon, however, will monotonically become both fainter and redder. I also think that it does asymptotically reach some value, rather than eventually increasing infinitely or decreasing passed some point in time. I'll have to get back to you on that.

Here's a nice review of distance measurements in cosmology.