The log
frontend is actually a stripped down version of [CLI Frontend]; it disables the usage of STDIN, so EOF from your SSH client won't make the session to exit.
For example, using the following shell script to keep a off-line log for your chat room
while true; do ssh -o BatchMode=yes -o ServerAliveInterval=60 example.com -l sshout -i .ssh/id_rsa_example log sleep 10 done < /dev/null >> sshout.log