I know pfSense boxes support monitoring an address to check a WAN connection is up and to let it know when to failover if another WAN link if available.
I can't remember of the top of my head but I think that specified address to monitor is also used to generate historical latency and packet loss graphs.
In addition, I remember finding a basic script on the net that would reset the box if a specified address was unreachable.
The bigger question is how you are going to know the remote routers are down if they are down adn unable to send you any info?
I used to look after a few remote offices on building sites so all sorts of problems could arise - I set up a central nagios box at the head office and used it to ping monitor the remote routers so it would be aware of any lines going down at any remote sites. If static IP's isn't an option, you could even use dyndns if supported to let you ping the remote routers.
Edit: Also let us know which brand/model router you are using in case someone on here knows of a method to do what you wish.