Rye bread freezes very well and it should keep for a couple of month without noticeable degradation. Over time, frozen breads tend to get ice on them, which can create some freezer burn, especially if they're sliced. Better bagging or waiting longer after they're baked/sliced might help.
I slice it then freeze the slices, so that all I have to do is take out as many slices as I need that day.