Best way to get IPv6 prefix?

I have a WNDR3700v3 running firmware V1.0.0.38_1.0.31, connected to Comcast. I get an IPv6 delegation via DHCP. My LAN has several Linux workstations/servers. All run Debian Stable, but some don't reliably pick up the IPv6 prefix and default route. I'd like to write a script to regularly poll the router and fix up the computer's IPv6 address (and update external dynamic DNS) when the prefix changes.

Other than screen-scraping  http://(router_ip)/IPV6_basic.htm , is there any way for a non-persistent user-level program to query the current IPv6 prefix?