But in a more general sense, what if for example current "emulator X" breaks support for "game X"?
The issue should be reported to the author so that he can fix it, in the case of FBNeo the fix will usually be available within a day. We can't fix issues we don't know about.
Do previous revision binaries get archived in some repository
No, if you want an older version, you would need to build your own binary using command line, or to find a backup.