This doesn't sound like a virus to me to be honest. The main way that your browser and the mail server recognises that you are signed in is via cookies. If you have a cookie in the browser memory, then you are signed in and if you don't, then you aren't. It might be that upon re-opening your browser, it encountered an error of some kind and the cookies were not recognised correctly.
What browser do you use? If after scanning your system with all three of those anti-malware products you find nothing, then there is probably little to be concerned about. However, if somebody else is accessing your mail accounts somehow, then you are best advised to change your password for each of them, ensuring they are strong and hard / impossible to guess.