After upgrading the first machine (the primary), you must manually repoint the configuration store before upgrading the secondaries.
Have a unique edge case? Consult the official Esri Support Pro (https://support.esri.com) or open a ticket with the ArcGIS Server team. Do not rely solely on community forums for production environments. upgrade arcgis server to 10.9.1
Symptom: After upgrading secondary machines, they fail to join the site. Solution: Hostname resolution failed. Edit C:\Windows\System32\drivers\etc\hosts to include the FQDN of the primary server. Restart the ArcGIS Server service. After upgrading the first machine (the primary), you