Rich,
My first guess is that somehow you accidentally set your browser to clear history whenever you shut it down. That will definitely cause this problem. Of course it will cause it any other place that you go to where you expect not to have to log in.
The second possibility is that your Profile/Password & Security could have gotten set to 2-step log-in. However, you would probably have mentioned what else happened, which is that when the browser takes you to H-M, it stops and tells you that it is sending a code to your email address of record, and you have to wait until that message arrives, copy the code (it's usually a 6 or 7 digit numeric string) and paste it into the offered field before you can proceed..
The third possibility is that the user ID or password stored in a cookie on your machine has gotten corrupted. The only fix for that one that I know of is to clear cache/History and start over from scratch.