SQL Server 2012 SP2 11.0.5058.0

Error message:

"TOP connection closed but a child process of SQL Server may be holding a duplicate of connection's socket. Consider enabling the TcpabortiveClose SQL Server registry setting and restarting SQL Server. If the problem persists, contact Technical Support."

"Error: 26073, Severity: 16, State: 1"

It seems it is a known issue for SQL server 2008 R2, but this is 2012. There is a other post regarding this, but no solution yet. Thanks in advance.

What is the OS version You have ?

When are you exactly getting this error ?

The TCP error 26073 occurs because SQL Server Native Client  handles a TCP close call on a socket incorrectly
 
When an application connects to SQL Server by using Microsoft SQL Server Native Client , you receive a "Non-yielding Scheduler" error intermittently as per different articles and posts. But I want you to make sure you are on latest patch on OS level as well as SQL level.

Apply the latest CU for 2012. IF you are on latest patch on both OS and SQL , I would recommend to contact MS Support Engineers.

Regarding to your description and error message you provided, which seems this issue occurs because SQL Server Native Client 10.0 handles a TCP close call on a socket incorrectly as you mentioned. 

If you tired all workarounds in the KB as you provided but still have problem, please post the SQL Server 2008 error log file. 

Alternatively you can try to install latest cumulative update: Cumulative update package 3 for SQL Server 2008 Service Pack 3. You can get from here: http://support.microsoft.com/kb/2648098