Loadbalancing proxies

You might be able to use a monitor that requests a response from a known Internet resource, like this one:

ltm monitor http /Common/bluecoat_www_check_HTTP1.1_200-OK_http {
    defaults-from /Common/http
    destination *:*
    interval 5
    recv "HTTP/1.1 200 OK"
    send "HEAD / HTTP/1.1\\r\\nHost:www.bluecoat.com\\r\\n\\r\\n"
    time-until-up 0
    timeout 16
}

If the Bluecoat handles this the same way as it would a regular client request this would tell you whether it still has a connection to the internet. Of course, if www.bluecoat.com goes down your clients won't be able to get to the internet...

Does the Bluecoat have its own monitor to detect connectivity to the internet? If so, you could create a monitor that reads that status directly from the Bluecoat.