Not that this is a solution to your problem, but I've had a few Linksys modems with this problem. Usually I am connected directly to the router so it's not a big problem and I haven't spent the time to try and fix it. But, when I did earlier on I couldn't find a solution. The problem seemed to be caused by "something" related to Yahoo Messenger which I used at my old job -- not at my new one in Georgia. And recently has occurred when I'm running my VPN client to the office.
My suggestion is to update the firmware and let us know if that resolves the problem.