The "or stops working" part is not part of rsyslog's description, and because it's so abstract most monitoring software lets you run a script to evaluate if the service has stopped working so you might as well just make your own service or crontab script, the core of which might look like this;
curl -s -m 5 "$URL" >/dev/null
if [ "$?" != "0" ] ; then
echo -e "Subject:Panic\n\nPanic" | sendmail -r me@domain you@domain
fi
