How are things set on the Power Schemes tab? If they're all still on the defaults, disable Standby, see if the problem persists.
If it does, set the monitor to Never, see if the problem persists.
If it does, set the harddisks to Never, see if the problem persists.
Or, if you don't want to spend three days doing that one-by-one elimination, set them all to Never and see if the problem persists.
If that doesn't fix things (or they're already all set to Never), what programs are running in the background? Is the computer connected to the internet through an always-on, high speed connection (cable or DSL)?