Here's one extreme idea that may work depending on the number of interfaces being used...
If your syslog server is located in the Trust Zone, off bgroup0, then what you can do is setup monitor track-ip from the bgroup0 IP to the syslog server. If the pings from bgroup0 IP to the syslog server fails, then bgroup0 interface will change to a DOWN state.
Of course, if you have other interfaces in the "Trust" zone then those interfaces will not be affected. Also, you can't monitor an IP address located in the trust zone from one of the untrust or dmz interfaces...
As mentioned already, a script might be a solution. Perhaps another server checking the health of the syslog server. If the syslog is unreachable, then SSH to the firewall and apply the deny all policy.
good luck...