When I use the iCloud calendar on my iPhone 5 and make an event with a reminder set to "on time of event", it will sometimes just beep and flash a notice on lock screen for a few seconds and then the notice disappear from lockscreen.
Sometimes though, everything works as it should and the notice is still there on lockscreen till I unlock the screen (or the event is over).
All settings in notice center and mail/calendar is correct.
When I use google calendar it always works!
The problem was there from iOS 6.0 and is still there after update to 6.1
I have been in contact with apple support who couldn't find any help at the moment.
More people seem to have this according to this site: http://forums.imore.com/ios-6/244349-ios-6-calendar-reminder-issues.html