Might Avast be checking all modified and changed files before shutting down?
You could test this by temporarily disabling that function and seeing whether shutdown speeds up.
But, on my computer, when I hit start/shutdown/restart, the first thing that seems to happen is that Avast shuts down and puts the little red x on its icon. I believe it's my firewall (Sygate Pro), that actually slows the shut down process...but it is impossible to be sure.
Louise