Like Ernest, I have never heard that expression "fall away" used like that.
The expression I'd use is "to grow apart", which means exactly what your examples intend: to gradually move to a less close relationship with someone (friend, partner, etc)
A similar one, more radical is to "fall apart". This has a meaning closer to "disintegrate", can be used to refer to things, or to relationships. But it conveys a much more drastic/dramatic change in circumstances than "grow apart", which is gradual.