through Earthlink I pay for the static IP service (which is really nothing more than a reservation in the PPPoE pool based on my username.)

it reboots itself (for no reason) and in doing so it grabs a new PPPoE address
Complain to Earthlink. You should never get any address except the one you've paid for. The fact that you are able to be asigned a different address is an indication that they've not done their job properly.
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Bitt Faulk