After having my first RRoD (I was lucky after having my first 360 for almost 5 years) I bought a new 250gb Elite. I connected it to my modem (which is a wireless router/modem combo) directly via cable. This is the same setup I had with my old 360. I transferred the data from my old hdd to the new device then deleted cache, system updates, and re-downloaded everything including profile. My modem is setup with open NAT. I get NO errors on network detection. I can log in to XBL immediately with no problems. If I use a service like Netflix if works fine so long as I'm watching something, but if I let it sit idle for a while or if I go into a single player game I get disconnected. This happens every time and takes roughly 10 minutes.
I have nothing else hitting the internet. My connection pulls roughly 25/5 reliably, better during the times I normally play. I have system idle set to 6 hours. I have deleted and re-downloaded everything twice. The only thing I will not do is set my modem to DMZ the Xbox because it's unneccesary to completely kill internet to the rest of my house (and fiancee) everytime I want to play on the 360. As mentioned before this is the exact same setup as with my old device and I never dropped connection. Everything else in the house runs fine, just XBL and pretty much when I play games in single player or not in dashboard and idle. Is there a system setting I'm missing?