We now have a call raised with Esri UK on this as it appears that something has changed recently in ArcGIS Online that has caused sync with AGOL feature services to stop working.
A few weeks back we were able to publish a feature service to AGOL and then add it to Mobile Project Center and use it within ArcGIS Mobile for Windows 10.2. However, if I try the same thing today I can publish the feature service, but when adding it to MPC it says 'Token Required'. If we try to access an existing AGOL feature service via ArcGIS Mobile 10.2 that was working fine, we get continually prompted for credentials.
I'll feed back anything I get from Esri UK.