I'm now starting to convince myself that maybe two sets of reminder messages are appropriate. One wave of reminders to be sent out 24 hours before the deadline, and another one to be sent out (to those who still have yet to submit final orders) 2 hours before.
The extra reminders shouldn't inconvenience anyone except those who are intentionally missing a turn (and what are you doing?!) But each reminder is independently useful. The 24-hour reminder gives you plenty of time to have a life outside of the computer, return to the computer and discover the reminder, and still have time left over to study your turn in case you haven't yet. The 2-hour reminder is a last-ditch effort to catch the attention of those people who may have seen the first reminder, and gotten distracted before they got a chance to do anything about it.
I think a 1-hour reminder would be too short to be consistently useful.
The only downside I can think of is that people may come to rely on these reminders, but email is not a particularly reliable medium to rely on.
David