I’ve dismissed several appointments but they keep coming back up in the Reminders Window.
Aside from deleting the appointment items (which I do not want to do), how can I dismiss these items permanently?
Deleting the appointments probably won’t help you here, nor disabling the reminder for the appointment. Outlook keeps an internal list of reminders which probably got corrupted somehow. To reset, start Outlook with the cleanreminders switch;
Windows Vista and Windows 7
Start-> type; outlook.exe /cleanreminders
Start-> Run-> type: outlook.exe /cleanreminders
Note: If that didn’t do the trick, it could be that you have a corruption in your pst-/ost-file as well. Scan it with the Inbox Repair Tool and then start Outlook with the cleanreminders switch again.