Looks like the prepackaged 'Exchange' service running on Android Marshmallow can't deal with being disconnected from the service for too long... If it is, it appears to crash and forget how to sync. It will perpetually say 'Last Sync at:' with the time it was last able to get data.

Even after you've fixed the outage it still won't reconnect. You have to manually remove the account under Settings->Accounts->Exchange and then re-add it again. Hopefully they fixed this bug in Nougat.