3393963 - How to analyse the error "RFC_ERROR_SYSTEM_FAILURE 'sapgui' start failed"

Logon to SAP Engineering Control Center (ECTR) fails with error "Connect to SAP gateway failed"

Example log:

[11:37:26.935] OMF-Q                Caused by: RfcException raised by system [XXX|systemname]:
[11:37:26.935] OMF-Q                    message: 'sapgui' start failed.
[11:37:26.935] OMF-Q                    return code: RFC_SYS_EXCEPTION (3)
[11:37:26.935] OMF-Q                    error group: 104
[11:37:26.935] OMF-Q                    key: RFC_ERROR_SYSTEM_FAILURE
[11:37:26.935] OMF-Q                    message class: 00
[11:37:26.935] OMF-Q                    message type: X
[11:37:26.935] OMF-Q                    message number: 341
[11:37:26.935] OMF-Q                    message parameter 0: RFC_ATTACH_GUI_FAILED
[11:37:26.935] OMF-Q                    at com.sap.conn.rfc.engine.RfcIoOpenCntl.RfcReceive(RfcIoOpenCntl.java:2041)
[11:37:26.935] OMF-Q                    at com.sap.conn.jco.rt.MiddlewareJavaRfc$JavaRfcClient.execute(MiddlewareJavaRfc.java:2032)
[11:37:26.935] OMF-Q                    ... 21 more
[11:37:26.935] OMF-Q                Caused by: com.sap.conn.rfc.exceptions.RfcGetException: 'sapgui' start failed.
[11:37:26.935] OMF-Q                    at com.sap.conn.rfc.engine.RfcImp.ab_rfcerror(RfcImp.java:1176)
[11:37:26.935] OMF-Q                    at com.sap.conn.rfc.engine.RfcGet.ab_rfcget(RfcGet.java:120)
[11:37:26.935] OMF-Q                    at com.sap.conn.rfc.engine.RfcRcv.ab_rfcreceive(RfcRcv.java:36)
[11:37:26.936] OMF-Q                    at com.sap.conn.rfc.engine.RfcIoOpenCntl.RfcReceive(RfcIoOpenCntl.java:1983)

SAP Engineering Control Center (ECTR), RFC error, SAPGUI , KBA , PLM-ECC , SAP Engineering Control Center (SAP ECTR) , Known Error