Here, so you don't have to babysit & to zero in on any outage windows a little better. Note I assume you're putting everything thru the VPN. If not add Cloudflare DNS (or whatever other IP/server you want to ping) to an approp. VPN policy:
mkdir -p /root/.bin/ # make a directory to store the shell script/sh
cat <<- '__EOF' > /root/.bin/pinger
#!/bin/sh
# shellcheck shell=sh
[ -n "$1" ] && TARGET="$1"
ping -4 -w '2' -q -c '2' "${TARGET}
ping_status="${?}"
[ "${ping_status}" = '0' ] || logger -t pinger "Ping to ${TARGET} failed [✘]"
exit 0
__EOF
chmod +x /root/.bin/pinger # make the sh executable
printf "*/5 * * * * /root/.bin/pinger '1.1.1.1' # ping cloudflare dns every five mins\n" >> /etc/crontabs/root
/etc/init.d/cron restart # restart the system timer to process every 5 min
logread -e 'pinger' will output any failed attempts including the timestamp.
Pro Tip
Update your .profile path to include /root/.bin so you can run it right after logging in via SSH by rand-hostname. See related below.