I had a variant of this issue where the messages slowly synced up to a point and then stopped altogether. It was solved based on @Michal_Burger 's info by checking the user’s page in the google admin console and un-suspending the user for going over Google’s bandwidth limit. On that user’s main page on the admin console, there was a large red banner at the top indicating that they were suspended along with a reset button. After unsuspending, the messages started flowing again within 2 minutes.