Windoze, Android and Wii all have the same behaviour - they appear to DOS the router with dhcp messages occasionally. BUT this is a result of poor connection to the internet, not the cause. The ancient DHCP protocol has a weakness in the fact there is no standard way for a dhcp sever to revoke a dhcp client lease. If you change something on the router - ip range perhaps or just reboot, it is up to the client to notice and to ask for a new IP.
Win7 etc do check their internet status continuously, wouldn't be surprised if this is by calling home, if the dhcp renew works to wake up the connection it avoids the IT support solution for all of "Turn it off and on again".
I don't know exactly what Asuswrt firmware does - it does have a connection monitoring app "wanduck". Tomato used to have a problem in that it didn't have an equivalent, so if ISP modem/router dropped the connection Tomato would not try to renew until its lease ran out - so I used to use a ping script to do the IT support equivalent. In developing such a script it is easy to see why Asus "wanduck" could be the problem - when ISP routers are overloaded or do 'traffic shaping/QOS' they can drop packets and de-prioritize icmp ping requests - easy to miss identify as broken connection. If the ISP modem is down it may revert to a local access mode, so it is important to check both local routes to the configured gateway and remote routes to somewhere real out on the internet.
If the wan is disconnected and reconnected all the comms passing through the router will be interrupted - sounds familiar?
