Thanks for your suggestions. I still have Web Shield and Mail Shield turned on, so (I think) anything coming into my computer from the outside world will be checked.
In all honesty, the web shield and mail shield are too late in the process (they aren't really looking for the same things), whatever gets on to your system. I'm also not sure if the Behaviour Shield would also be impacted by disabling the File Shield or not.
Content that makes it down past the Web and Mail Shields won't be scanned by the File System Shield when they are active.
Have you made any changes to the default options in Avast Antivirus ?
I really think you should try to clarify, exactly what is being scanned, is the Smart Scan really running as by default (as far as I'm aware) it shouldn't. I haven't seen a Smart Scan on my system other than if I run it (usually as a result of a question in the forums).
So I just ran a Smart Scan and towards the end it asks if you want to run a scheduled scan ensure that is unchecked.
Personally the Smart Scan is more a vehicle for offering more Avast paid programs.
Another option would be to do a clean reinstall of Avast including running avastclear, restarting your computer and reinstalling Avast.