I managed to track down a related question on the BlackBerry forums which helped me solve the problem. Here are the steps:
- Open Contacts app
- Click BlackBerry button
- Type "RSET" (there's no dialog box, just type it straight on the screen)
- Confirm that you want to delete the list which is not configured for wireless sync. This will delete the entire contact list and it's contacts
- Confirm you wan to resynchronize the list is is configured for wireless sync. This will delete and redownload all your contacts.