Try starting Outlook once with the /cleanreminders command switch if your
version of Outlook (which you decided wasn't important enough to mention)
supports it.
I have a user with a similar problem. I tried that switch before but
the meeting reminders still don't pop up. In Outlook, the setting is
set for Default Reminder to be 15 minutes. I sent the user multiple
meeting requests and I checked when the meeting comes into the inbox
and after I accept the meeting to see if it would make a difference,
it did not. The check box is not checked for that meeting to remind
me. The meeting was sent with the meeting reminder set. The user has
to manually check the box on every meeting after he accept them to set
the reminder.