I managed to get local notification when iBeacon (using Kontakt Beacon) enter a region in Background mode . at the same time I monitor 3 beacon regions with specific & unique Identifier (each has same UUID but unique Major and Minor combination). In Lock Screen Mode, my app can notify when these beacons present, but I don't know why even the beacons and my app all stay still almost next to each other, the delegate DidExitRegion is still called, please look at my Log.
2014-01-18 11:56:49.828 sunlandbeacon[1385:60b] Enter Inactive mode
2014-01-18 11:56:49.848 sunlandbeacon[1385:60b] EnterBackgroundMode with Badge 0
2014-01-18 11:57:28.629 sunlandbeacon[1385:60b] Exit a beacon range
2014-01-18 11:57:29.305 sunlandbeacon[1385:60b] Local Notification Happens with Badge 1
2014-01-18 11:57:29.307 sunlandbeacon[1385:60b] Enter Region 1 with flagvalue 1
2014-01-18 11:58:15.173 sunlandbeacon[1385:60b] Exit a beacon range
2014-01-18 11:58:15.176 sunlandbeacon[1385:60b] Exit a beacon range
2014-01-18 11:58:15.178 sunlandbeacon[1385:60b] Exit a beacon range
2014-01-18 11:58:15.880 sunlandbeacon[1385:60b] Local Notification Happens with Badge 2
2014-01-18 11:58:15.886 sunlandbeacon[1385:60b] Enter Region 1 with flagvalue 1
2014-01-18 11:58:16.175 sunlandbeacon[1385:60b] Local Notification Happens with Badge 3
2014-01-18 11:58:16.184 sunlandbeacon[1385:60b] Enter Region 2 with flagvalue 2
2014-01-18 11:59:02.784 sunlandbeacon[1385:60b] Exit a beacon range
2014-01-18 11:59:02.787 sunlandbeacon[1385:60b] Exit a beacon range
2014-01-18 11:59:02.790 sunlandbeacon[1385:60b] Exit a beacon range
2014-01-18 11:59:03.491 sunlandbeacon[1385:60b] Local Notification Happens with Badge 4
2014-01-18 11:59:03.493 sunlandbeacon[1385:60b] Enter Region 1 with flagvalue 1
2014-01-18 11:59:03.792 sunlandbeacon[1385:60b] Local Notification Happens with Badge 5
2014-01-18 11:59:03.796 sunlandbeacon[1385:60b] Enter Region 2 with flagvalue 2