I would report this directly to the project responsible, but it's hard knowing which project would be responsible (Cygwin, Git, or Git for Windows which creates the git.exe I am using. This isn't Cygwin git, it's Git for Windows.)
Using the windows command prompt, git add -i [filename] works as expected. There's a slight hang before it shows the prompt, but nothing to be concerned about.
Using Cygwin (64), the same command just hangs indefinitely. After investigation I have determined that it launches a copy of perl.exe, which then maxes out a CPU but doesn't seem to return.
Here is another Git/Cygwin/Perl question, but unfortunately doesn't directly solve my issue: cygwin cannot exec 'git-add--interactive' permission denied