Attempts to sign in to ArcGIS Maps for Office on the portal machine and with the option to "Fall back to cloud resources" unchecked causes the sign-in page to display the following message:
"Sign in to the ArcGIS platform. Page not found".
This issue occurs because the portal machine does not have Portal Resources for ArcGIS Maps for Office installed, or if the installed version is outdated and not compatible with ArcGIS Maps for Office.
This issue can be resolved by ensuring Portal Resources is updated accordingly whenever ArcGIS Maps for Office is updated as well. To determine the version of Portal Resources, an entry of the installation can be found in the Windows Control Panel.
The default installation directory is:
C:\Program Files\ArcGIS\Portal\webapps\docroot\resources\arcgismapsforoffice\x.0\office\<version number>