Hi Jyrki,
I've run a test on my side, but can't reproduce the issue. To find the root cause of the issue, I'd like to collect the following information:
1. Whether the calendar exists if the user re-start the Outlook.
2. Whether the calendar meeting still exists on the User's Outlook Web App(OWA).
3. When did the issue start?
In addition, I suggest the user configure the Office 365 account on a new profile and check to see if the issue persists.
How to create and configure email profiles in Outlook
http://support.microsoft.com/kb/829918
Set up email in Outlook 2010 or Outlook 2013
http://office.microsoft.com/en-001/web-apps-help/set-up-email-in-outlook-2010-or-outlook-2013-HA102823161.aspx?CTT=1
Please post the results here for further troubleshooting.
Thanks,
Aaron Yuan