Is it only since IE6? Or did it happen even before then?
Check with the rest of the family. My Dial up used to do it years ago when people started to use the phone as it was a wireless unit so it would interfere with the signal somehow. This cut off the internet of whoever was online at the time.
Otherwise I suggest unplugging phones to be sure it isnt any dialer or other features that some of these new phones have.
Other than that Im without a clue.