I found the below in the Windows Application Log.

Service cannot be started. Microsoft.ReportingServices.Diagnostics.Utilities.ServerConfigurationErrorException: The report server has encountered a configuration error. ---> System.Xml.XmlException: The 'SemanticQuery' start tag on line 210 does not match the end tag of 'Extension'. Line 229, position 6.

I came across the answer here:

https://social.msdn.microsoft.com/Forums/sqlserver/en-US/e5a8ab58-1382-4509-8349-a8aab418bd88/ssrs-forms-authenitcation-error?forum=sqlreportingservices

The issue was that someone had commented out a single line in the config file while trying to address an error related to TERADATA. That left a syntax error in the config file. As soon as I corrected that the SSRS Config Manager again showed the missing instance in the Connection drop down.