AW has an automatic timeout (currently 20 minutes), not too inconvenient generally but unhelpful for some people if you might be waiting on a reply from a prossie.
Chrome has this addon available:
External Link/Members OnlyFirefox offers:
External Link/Members OnlyAlthough there's a tab on AW that will tell you if you have new messages even when you are logged out, you still have to click it and it still doesn't tell you what the message is until you log back in.
Still trying them out, but both add-ons quit when you quit the site as far as I can see. Maybe helpful for the non-paranoid non-wife-whipped.