I have *exactly* the same issue..
Everytime there is an outage, it gets resolved, and then I have a horrible time getting a new dhcp lease. The link comes up fine, the wifi router gets the temporary lease from the 8200 modem fine (meaning dhcp is fine on the router) but when the temporary lease expires after 20 seconds, and the permanent public lease is requested, no response is received.
I can reboot the cable modem (remotely or locally), the router but nothing will specifically fix it.
I even got a separate cable modem (Netgear so different brand). This has the exact same symptom (works fine until an outage, then no dhcp response), so it isn't the modem, isn't the 'settings' and isn't the router either because even directly connecting a PC instead of the router, doesn't change the dhcp behavior.
It is intensely frustrating, and appears to be a remote dhcp problem (the dhcp server is 220.127.116.11 btw) but trying to get xfinity to understand this is a challenge at the least.
The only way to fix it is lots of cable modem reboots/cable resets and waiting eventually for the dhcp server to respond which usually it does after a few hours of trying. Just waiting passively though does nothing, as I have left it for a day before without any change (lots of unresponded dhcp requests). If you ever get a resolution.. please share!!
kiwigirl, are you able to test this on another computer? Have you attempted to flush DNS via the command prompt?