After upgrading the Core server to versions 6.1.3 or 6.2 many SQL servers are having their SQL instances yellow with error that Core is unable to authenticate properly. Agent software version is 5.4.3
Outdated agent software
To resolve the issue, agent software should be upgraded to the same version as the Core. Please note that upgrading agent software requires a reboot.
Inability to communicate with the SQL instance does not mean that backup will not be taken. Agent software initiates SQL VSS writer to make sure that databases are backed up in a consistent state. Without initiating VSS, backups are taken for files as is, using disk VSS writers.