My best guess is a problem with UPnP and the IP the router is giving the Xbox. But to be honest, it sounds like maybe your looking for a easy answer and I don't think I can provide one. Do you have anyone, a friend or family member, that might be able to help? Im willing to help of-course, but it would mean logging into the router and changing some settings. Is this something you want to and/or are allowed to do?
I've been experiencing the same issue for at least two months. I moved here from the east coast where I had Comcast. I never had the issue there.
I'm a pretty technical person (Linux Sysadmin) so I know it's not something obvious. I've also done a fair amount of testing. I might enable syslog logging to see what's going on in the backend and/or setup smokeping to confirm it's not just xbox that's experiencing issue. But I'm pretty sure it's not. My girlfriend connects to remote servers via SSH and those connections seem to drop fairly regularly as well.
Very frustrating to say the least. Especially when I'm about to get a score streak in Call of Duty and BAM-- disconnected!
Glad I'm not the only one though...
EDIT: Also, just fyi... I'm wired directly to XBOX.