Ok, possible work-arounds come to mind.

1:Try adding the browser processes to the Trusted processes list in the Behavior Shield’s expert settings.

2:Try disabling the Script Shield.

3:Try disabling the Web Shield.

Try these one at a time, attempting to shut down again after each change. And also make sure to undo the previous changes after each attempt, you want to try and isolate what part of Avast! might be causing this.