All of a sudden I could not sync one of my calendars with my iPhone or Thunderbird any more. Since all my other calendars would sync as normal, it probably could not be a problem of my server configuration. While the calendar was shown in the web interface properly, I discovered that I could not export the calendar as well.
Then I found this: https://tigr.net/4346/2015/09/03/broken-events-in-owncloud-calendar/
Indeed, my database contained one entry with invalid data which caused all the trouble.
Using the following MySQL query, I could detect the broken event:
SELECT * FROM oc_clndr_objects WHERE calendardata NOT LIKE ‘%END:VCALENDAR%’;
After deleting the database record containing the invalid data everything worked fine again.