Hi - In my distributed deployment, I too began experiencing the same error: "Database server found to be stopped. Restarting it". When this was infrequent, not a big deal..... but recently this began to occur with much greater frequent and has now interrupted both data writes and the portal backup routine when the postgres is offline. Obviously.
In our case, we use McAffee. We found that by removing the ArcGISPortal.exe and the postgres.exe processes from active McAfee inspections (I think its the McAffee Adaptive Threat Protection Service) and adding them to the trust exclusion that has now eliminated this issue. So similar to the Carbon Black issue identified above by Michael Schoelen. I also told our security team that these processes along with all the other core processes used by server, datastore, and portal should be trusted and not inspected, per all the help docs. Jonathan Quinn and Michael Volz thought you guys would like to know as well....