Linksys Wireless Router :: EA4500 Internet Port Cycles On And Off Every Few Seconds

I bought a EA4500 to replace my old WRT54G earlier this year. At first the router worked fine. After the automatic firmware upgrade to Cisco Connect Cloud, I was never able to get the Connect Cloud stuff to work, constant 500 Internal Server errors when trying to access the router with the Internet cable attached.  So I downgraded back to the old firmware and all was well again. Then I started having problems a few months ago, when I would wake up in the morning, the router would be cycling the Internet port on and off. I could usually reboot everything and it would work the rest of the day. I lived with it like this a while, and support couldn't seem to find anything wrong. Eventually it started getting worse, until the point I could hardly ever get it to stay connected. I got Cisco to RA the old router and I figured problem solved. Now while the EA4500 was gone, I used my WRT54G again, and everything worked fine for nearly two weeks while I was waiting on the replacement EA4500.

So today the new EA4500 showed up, I connected and configured it, and it worked for a short time. Then suddenly I lost Internet, looked up at the modem and the LAN light was going on and off every few seconds. So I'm back in the same boat as before.I've tried changing cables, same setup works fine with the WRT54G. Modem works fine with WRT54G and connected directly to the computer, zero problems. I tried lowering the MTU, turning on MAC address cloning, and various other things.My modem is a HughesNet HN9000.