SQL Server: Frequent Login timeout expired in Linked server
I am here answering my own question. After so many observations and experiments with searching over the internet, I found solution to this issue. You need to run this simple query

USE Yourdatabase;
GO
EXEC sp_configure 'remote query timeout', 0 ;
GO
RECONFIGURE ;
GO


The setting takes effect immediately without restarting the server.

Please refer Configure the remote query timeout Server Configuration Option and sp_configure.