Safari loses web site "login" state after computer restarts
I seem to have resolved this problem by unchecking the "Reopen windows when logging back in" box on the restart dialog.  Once I did that I was able to log back in and then run Safari without it losing my site logins.  

Interestingly I was then able to re-enable that checkbox and restart again without issue, so it seems that something in the restore process was borked.