Just for S&G's I called Earthlink. This time their official response was:

"It may be due to incorrect release of IP address by your modem."

In other words my router reboots, requests an address. The PPPoE, server seeing that my modem is still active, is not smart enought to realize that I should get the same address and issues another.

I should just reboot a couple hundred times and see if I can use up their pool

So naturally I asked "How do I correct this issue?"

"Your modem will not release the IP address because abrupt shutdowns etc."

Again I'm back to a need for a router that doesn't reboot.

Damn!