After a lot of troubleshooting, I now believe my server is causing my router to flap up and down.
I pinged the router all night and it showed zero packet loss, but after pluggin in my server, it's up and down like a yoyo. I have tried using Wifi instead of via patch lead, but with the same result.
What could be causing this? I tried downloading ethereal to monitor the traffic, but their installer seems to be corrupt no matter what mirror I chose.