Resolution:
When the adapter configured for a TRFC receives a request from SAP, it throws the following error:

AER3-000113 Performing one way invocation on the server tracking=#-0Y--C--GAYfJ-dw-3060c-Mb-2BY#
2008 Sep 11 19:59:40:875 GMT +5 SAPAdapter.AdapterForQRFCOutBoundTest Error [Adapter] AER3-000410 Server thread exited, message : Illegal operation  
2008 Sep 11 19:59:51:500 GMT +5 SAPAdapter.AdapterForQRFCOutBoundTest Info [Adapter] AER3-000400 Invalid connection detected. Message :  

This error is due to the RFC being downloaded as a request reply RFC in designer.

Please note that in case of TRFC, the RFC has to be downloaded as a one way rfc while downloading the schema of the RFC.

The error occurs because the invocation sent from SAP is a one way RFC request but the RFC is a Request reply in Designer.
Please download the RFC as One way by selecting the invocation protocol as "One Way" in Designer to eliminate this error.