I had the same problem and it was quite annoying. What you need to do is set the time so that it is before midnight on the day before a contest. (I set it 15 minutes before just to make sure it would work). Then your all set to go. I suggest saving before you do the contest just in case you lose.
Reminder: Contests are Sat. Tues. and Thurs. (my game was originally on Saturday and I changed it to 11:45pm on Wednesday.)