Idle time quick scans are dependent on a certain type of Norton update. Once this particular update is processed, then a timer is triggered. And a quick scan will be initiated in the background.
It happened to me half an hour ago while I was actively browsing! First time I've noticed it happening. I had connected and did the manual LiveUpdate three hours earlier.
Usually for me, once I'm offline, a quick scan will occur only once until I'm online again for a LiveUpdate. The evidence lies in the page faults reported in taskmanager for the ccsvchst.exe (all users). For me, it's about 3 million per quick scan.