How to continuously monitor output of shell command? Should I use Bash or Ruby?

The problem may be that the output is buffered. You may have luck with the util "stdbuf" to disable the buffer. (another tool is "unbuffer") You can fully disable all buffers with:

stdbuf -i0 -o0 -e0 [command] # 0 is unbuffered and L is line-buffered

Your command might look like this:

stdbuf -oL -eL ios_webkit_debug_proxy |& tee -a proxy.log
tail -f -n0 proxy.log | grep --line-buffered "Disconnected" | while read line ; do [restart server] ; done

I tested it with this:

# This is one terminal
cd /tmp
echo > log

# This in another terminal
cd /tmp
tail -f -n0 log | grep --line-buffered "disconnect" | while read line ; do echo "found disconnect" ; done

# Then, in the first terminal
echo "test" >> log        # second terminal does nothing
echo "disconnect" >> log  # second terminal echos "found disconnect"

The tail -n0 is because if the tail reads a disconnect in a log file that already exists, it will restart the server as soon as you run that command.

EDIT: stdbuf is overridden by tee (see man tee). You may have more luck in a different format but some stuff to play around with:

stdbuf -oL -eL ios_webkit_debug_proxy 2>&1 >> proxy.log
# or
unbuffer ios_webkit_debug_proxy |& tee -a proxy.log | grep --line-buffered "Disconnected" | while read line ; do [restart server] ; done