If your appointments disappear from your iPhone's Calendar app, the culprit is almost always the sync settings. The iPhone automatically deletes old appointments if you have synced the Calendar app with iCloud or another calendar sharing service. The other likely possibility is that if you have shared your calendar with someone else, that person has editing permissions to add or delete events from the shared calendar.
Syncing and Past Events
If you have synced your iPhone with iCloud or another calendar service, the iPhone may automatically delete old events. To prevent this from happening, launch "Settings" on the iPhone; select "Mail, Contacts, Calendars," and then scroll to the bottom and select "Sync." Select the time period for which you want to keep old appointments. These range from two weeks to six months. To keep past appointments on the iPhone indefinitely, select "All Events."
Shared Calendar Events
If you share a calendar loaded onto your iPhone with a coworker or family member, that person can delete appointments if you have used the default "Allow Editing" option. To turn this off, launch the Calendar app, select the calendar being shared and tap "View & Edit" beside the person's name. Tap the "Allow Editing" button to toggle it off.
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