Problem: Environmental variables show that the server is present for the version of Revit in question, but there is no server access within the application. Other versions of Revit besides this one have server access.
Workaround:
Browse to the program files for the Revit server for the version of Revit that is missing server access. In this case, it's 2015. Open the config folder.
C:\ProgramData\Autodesk\Revit Server 2015\Config
If it is missing the RSN file, you may be able to copy it from a config folder of a different version. Look in the config folder for a version that has functioning server access.
In this case, the RSN file is present in the 2016 version. Copy this file and paste it into the config folder for the offending version of Revit.
Open the version of Revit which didn't have server access, and check that it's working.