This is a complete and total stab in the dark. Truly.

Have you tried the ipconfig trinity of commands? It sounds like something inside the SE server farm isn't updating when it should in terms of routing and name resolution. By running the ipconfig trinity you're forcing your computer to get new routing information, thereby fixing whatever isn't getting updated. Just my take on it.

Considering this seems to rear it's head every 7 days or so I'd say a server machines ip address is on 7 day lease and therefore on a renew is getting changed but the routing info isn't being spread to the clients.