If I get unexpectedly logged out of my email account, even if I can log right back in, this should already be at "something seriously fishy is going on and I need to investigate immediately", such as checking the account for any activity. Not being able to log in to my email is "check my provider's status page to make sure they're not having a widespread outage, and if they're not, get on the horn with support immediately".
As the author says, your email account is the keys to the kingdom for virtually every other account you have. Anything that threatens it is serious business.