Well here are a few questions:
Do you have a firewall/router?
When using Linux, do you usually have some program that always uses the net (f.e a irc client)?
The reason I ask this is because I know with my ISP if I am inactive for a few hours they turn down my Internet speed to give to people who will actually use it. I use to have to restart my computer to get full speed back up, thought it was just Windows
Anyway, my firewall/router changed that, because it would I guess trick them into thinking I'm still using the net.
Something like a IRC client may help, as it'll always be sending and receiving information.
Hope this helps