I have a prediction that I will encounter this error at 4:00 PM today my time and not a moment sooner. I will tell you why. The GMT date will change at 4:00 PM today to February 5th, whereas I and my server will still be in February 4th.
Somewhere in your session handler, you are probably comparing date/time based on time alone, assuming the date is the same, but since there is a mismatch of the day it produces an error.
Furthermore the error seems to go away after 11:00 PM my time, which is 12:00 AM my server's time which is a new calender day that matches what GMT's day currently is.
I bet if I change my servers time to GMT and my Joomla time to GMT, the error will go away. I can easily test this.
Are there any error logs I can turn in to you that would give you any indication what is going on?