I found out that using ssh.exe from the Git package works every time, as opposed to the ssh that comes with cygwin (the default).
Using this exported variable seems to help; it’s slower (2x or more) but it’s more stable. Take it as another workaround.
$ export GIT_SSH=/cygdrive/c/Program\ Files/Git/bin/ssh.exe
FYI:
This version of Msysgit comes with OpenSSH 4.6p1, OpenSSL 0.9.8e. [works]
Cygwin’s SSH is OpenSSH 5.5p1, OpenSSL 0.9.8n. [doesn’t work]