I was actually going to say the same thing a while back, but got a bit confused when I saw some script shield activity every now and then (in between long bouts of inactivity).
From my observations this applied to earlier versions of avast! since IE9 was released and also affects me (a user of Win 7 x64). This was dramatically noticeable after the update to IE9 as almost immediately I noticed the statistics in Script Shield activity drop to 0 for long periods of time (never was like this before). It only seems to pick up again following full system scans or something more intensive related to 3rd party applications (can't say for sure). However, it is quick to die down to no activity afterwards.
I don't use IE a lot, but whenever I do it's the 32-bit version. I'm aware I have some programs that use it such as MSN messenger, but that hasn't stopped the Script Shield from functioning actively prior to the IE9 update.