I think you should change the warning and critical values in the check_ping to something that fit your needs.
Try to ping from your host “per hand” and look at the response times and the losses. Maybe there are some problems on your router.
Try check_icmp and write your own service check => check_ping with other defaults!
change to your libexec directory make a and execute the command check_icmp per hand. If you’re not familiar with the params, then try -h. This is what I have done. Then watch at the answers.