I had this same problem. I have the linksys BEFSR41 router.
Well, its not your router, I'll tell you that much. I mean, it may, but its the service screwing up. They're supposed to renew your DHCP lease, and I'm betting that they're changing your IP address every so often. In my case, it was every 15 minutes which really pissed me off. If you watch, they might not even change your IP address, only renew the lease. if thats the case, you need to contact them, explain to the Tier 1 guy that you have an IP issue so they'll transfer you to Tier 2, re-explain yourself and tell them you've done everything possible and you'd like a callback from the Tier 3 guy. If/When the Tier 3 guy calls back, you need to ask him to rip/rebuild the routers, he'll be confused for a second, because this isn't a common request and he probably doesn't handle it. He can however, give you the number of the office that handles their main routers. If you get that number, put it under your pillow and keep it forever. (should your service be SBC, let me know at mhiser@sbcglobal.net and I can give you this number directly) So call this guy up, (becareful, he's not a low level CSR, this guy is completely certified and knows what he's doing) explain to him your problem and that you would like to have your information ripped from the routers and rebuilt. It takes about 2 minutes and more than likely he'll do it for you. It solved my problem after 3 months of dealing with the CSRs.
Riser