It seems that I can cause the router to reboot by running Namebench with router IP configured as a potenital DNS server. The Log messages just before the reboot:
Mar 9 17:19:25 2014 Wireless_Broadband_Router Unable to change DSCP of icmp socket to value 0 for ping Socket operation on non-socket
Mar 9 17:19:28 2014 Wireless_Broadband_Router Packet too short: 12 octets
Mar 9 18:19:49 2014 Wireless_Broadband_Router last message repeated 2 times
Mar 9 17:19:33 2014 Wireless_Broadband_Router The system is going DOWN for reboot.
This and the fact that it ran for 10 days straight while no machines were running ( I was on vacation) leads me to believe that the router is not able to handle certain types of traffic.