Sync new contact back to Outlook

[AC Question]

When I add a new contact or modify existing one in Contacts app, it doesn't sync back to my Outlook.com and Office 365 contact list. In fact, they disappear completely after a while. I presume this happens because they get overwritten by Outlook/O365 contact list. Basically, only one-way sync is possible. Any help? I have Moto E 2nd gen running 5.1. TIA.