Hi JesperBaldur,
Based on your description, I would like to confirm the following information:
1. If the issue occurs on both internal and external users, or just some specific users?
2. Does the issue occur at other users in the same Office 365 tenant?
You can try the following suggestions:
1. I suggest you send an attachment with doc or xls file to see if the issue existed.
2. Please try to create a new profile and re-add the account in Outlook to see if the issue will persist.
How to create and configure email profiles in Outlook: http://support.microsoft.com/kb/829918
Connect Outlook to This Account: http://help.outlook.com/en-us/140/dd253202.aspx
Thanks,
Anna Shi