Below the Error Log Reported in SQL Agent (64 bit SQLServer 2008R2 Enterprise Edition Service pack 2 ,32Core CPU Numa Node and 64GB Ram 

[298] SQLServer Error: 10054, TCP Provider: An existing connection was forcibly closed by the remote host. [SQLSTATE 08S01]

[298] SQLServer Error: 10054, Communication link failure [SQLSTATE 08S01]

[165] ODBC Error: 0, A network-related or instance-specific error has occurred while establishing a connection to SQL Server. Server is not found or not accessible. Check if instance name is correct and if SQL Server is configured to allow remote connections. For more information see SQL Server Books Online. [SQLSTATE 08001]

[382] Logon to server '(local)' failed (ConnUpdateStartExecutionDate)

Can some one help me please 

I have alternate solution to restart the SQl Agent every time  when this situation arise on my production server.

Its Occur on my production server 2-3 times in a week

Hi Naveen,

According to your description, you are experiencing "SQLServer Error: 10054, TCP Provider: An existing connection was forcibly closed by the remote host. " issue when running a job, right?

There can be a number of reasons for the SQL Connection to be lost between the SQL Server and a client workstations, including but not limited to:

• Workstations set to Stand By, Sleep or Hibernate when not used for a period of time.
• Timeout settings on SQL Server, disconnecting idle sessions.
• Faulty network infrastructure causing the connection to the server to be dropped. This includes bad Wireless quality.
• Not installing critical updates, causing a faulty network driver to drop the connection.
• The Database Property under Options "Auto Close" was set to True allowing the server to close "inactive" connections. This must be set to False.

Here is a blog which describes this issue detaily, please refer to the link below.
http://blogs.msdn.com/b/developingfordynamicsgp/archive/2013/12/04/tcp-chimney-setting-and-sql-server-error-tcp-provider-an-existing-connection-was-forcibly-closed-by-the-remote-host.aspx

Regards